Question

Need help using Matlab to solve differential equations, will rate! Thank You!

a) The code used to solve each problem b) The output form c) Use EZPLOT (where possible) to graph the result Use Matlab symbolic capabilities to solve the following Differential Equations: yy +36x = 0 3. ytky = e2kakis a constant y" +(x +1)y = ex'y' ;y(0) = 0.5 4 4y-20y'+25y = 0 xy-7x/+16y=0 xy-2xy'+2y=x' cos(x) yy =292 y-4y'+4y = (x + 1)e 2x

Answer 1

Please find following MATLAB code, ouput and the Ezplot (wherever possible) for all parts. We have used dsolve() function in MATLAB to solve Symbolic solution of ordinary differential equations.

Part 1:

MATLAB Code:

% Part 1
syms y(x)
ode = diff(y,x)*y == -36*x % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

The screenshot of the result:

Command Window ode (x) - y (x) *diff (y (x) , x) --36#x 2 (1/2)18*x2 C2) (1/2)

PART 2:

MATLAB Code:

% Part 2
syms y(x)
ode = exp(2*x)*diff(y,x) == 2*(x+2)*y^3 % diffrential equation to be solved
cond = y(0) == 1/sqrt(5); % set the initial condition
ySol(x) = dsolve(ode,cond) % solve the function
ezplot(ySol(x)) % plot the solution

-----------------------SAMPLE OUTPUT

Command Window ode (x) exp (2*x) *diff (y(x), x) y(x) 3* (2*x 4) ySOI (x) (2 (1/2)((2*exp (2*x)) (2*x 5)) 1 (1/2))/2

(21/2 (2 exp(2 x))/(2 x +5))1212 80 70 60 50 40 30 20 10 0 -2 6

PART 3:

MATLAB Code:

% Part 3
syms y(x)
k=10; % value asssigned to constant
ode = diff(y,x)+k*y == exp(2*k*x) % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function
ezplot(ySol(x))

----------------------------------SAMPLE OUTPUT

Command Window ode (x) - 10*y(x) + diff (y (x), x) -exp (20*x) exp (20*x)/30 + C1*exp (-10*x)

exp(20 x)130+C, exp(-10 x) 4 -2 -4 -6 -2 6

PART 4:

MATLAB Code:

% Part 4
syms y(x)
ode = diff(y,x)*((x+1)*y) == exp(x^2)*y^3 % diffrential equation to be solved
cond = y(0) == 0.5; % initial condition set
ySol(x) = dsolve(ode,cond) % solve the function

------------------------------------SAMPLE OUTPUT

Command Window ode (x)- y (x)diff (y(x), x)( 1)exp (x*2) *y (x)3 -1/ (int (exp (y"2 ) / (y + 1), y, 0, x, 'IgnoreSpecialCases", true, 'IgnorennalyticConstra ints', true) -2)

Note that ySol(x) here indicates that the result obtained here has been evaluated through special cases, the details of which have been mentioned along with.

PART 5:

% Part 5
syms y(x)
ode = diff(y,x)+y == x % diffrential equation to be solved
cond = y(0) == 4; % initial condition set
ySol(x) = dsolve(ode,cond) % solve the function
ezplot(ySol(x)) % plot the solution obtained

---------------------------------SAMPLE OUTPUT:

Command Window ode (x) diff (y (x), x) + y(x) x ySOI(x) = x 5*exp (-x)1

x + 5 exp(-x) 1 1000 900 800 700 600 500 400 300 200 100 -2

PART 6:

MATLAB CODE:

% Part 6
syms y(x)
ode = 4*diff(diff(y,x),x)-20*diff(y,x)+25*y == 0 % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

-------------------SAMPLE OUTPUT:

ode (x) 25*y (x) -20*diff (y (x), x) + 4*diff (y (x), Х, x) -0 ySol (x) c1 * expl (5*x) /2 ) + C2*X"exp ((s*x)/2)

PART 7:

MATLAB CODE:

% Part 7
syms y(x)
ode = diff(diff(y,x),x)-diff(y,x)+y == 2*sin(3*x) % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

--------------------------------SAMPLE OUTPUT:

ode (x) y(x) -diff (y (x), x) + diff (y(x), Х, x) -- 2*sin ( 3 *x) cos ( (3 (1/2) x)/2) (3 cos (3x- (3 (1/2)*)/2)73(3*cos (3x (3 (1/2) x) /2)/73 (8 sin (3*x- (3 (1/2) *x)/2)/73 -(8sin (3x3 (1/2)x) /2))/73 (

PART 8:

MATLAB Code:

% Part 8
syms y(x)
ode = x^2*diff(diff(y,x),x)-7*x*diff(y,x)+16*y == 0 % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

----------------------------------SAMPLE OUTPUT:

Command Window ode (x) = 16*y (x) x 2 diff (y(x), x, x) - 7*x*diff (y (x), x) 0

PART 9:

MATLAB CODE:

% Part 9
syms y(x)
ode = x^2*diff(diff(y,x),x)-2*x*diff(y,x)+2*y == x^3*cos(x) % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

-----------------------------SAMPLE OUTPUT:

Command Window ode (x) - 2*y(x)+ x 2 diff (y (x), x, x) - 2*x*diff (y (x), x) x*3*cos (x) yS01 (x) C1*x x*2*sin (x) C2*x*2 - x* (cos (x) + x*sin(x))

PART 10:

MATLAB CODE:

% % Part 10
syms y(x)
ode = y*diff(diff(y,x),x) == 2*diff(y,x)^2 % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

------------------------------------------------SAMPLE OUTPUT

Command Window y (x) *diff (y (x), X, X) -2 * diff (y(x) , x) ^2 ySol (x) = С5 -1/ (C3 C1*x)

PART 11:

MATLAB Code:

% Part 11
syms y(x)
ode = diff(diff(y,x),x)-4*diff(y,x)+4*y == (x+1)*exp(2*x) % diffrential equation to be solved
ySol(x) = dsolve(ode) % solve the function

---------------------------------------SAMPLE OUTPUT

Command Window ode (x) 4*y (x) -4*diff (y (x), x) + diff (y (x), Х, x) -exp (2*x)* (x + 1) Sol (x) - CI * exp (2 *x) + (x^ 2 * exp (2 *x)*(x + 2)) /2 + C2*X"exp (2*X) (x"2 * exp (2 *x)*(2*x + 3)) /6 -

For more details regarding working, other examples and syntax information, please write 'help dsolve' in command window of MATLAB.