Solve the following ODE's for Y(x)
A) x2y''-2xy'+2y=0
y(1)=2 y'(1)=1
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Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
Solve the following ODE's for Y(x) A) x2y''-2xy'+2y=0 y(1)=2 y'(1)=1
use the fact that y=x is a solution of the homogeneous equation x^2y''-2xy'+2y= 0 to completely solve thee differential equation x^2y''-2xy'+2y= x^2
Solve the following Bernoulli equations: a) x2y' + 2y = 2e1/xy1/2 answer: y = e2/x(c-1/x)2 b) xy' + y = x4y4 y(1) = 1/2 answer: y = 1/x(11-3x)1/3
1.Find the general solution to the following ODE's a). y'' +y= sec^2t b). x^2y'' +3xy'+3y=0
15. (2xy + y^2 ) dx + (2xy + x^2 − 2x 2y^2 − 2xy^3 ) dy = 0
2. Solve the differential equation (2xy + y)dx + (x2 + 3.ry2 – 2y)dy = 0. Answer: x²y + xy3 – y2 = C.
For the following Euler-Cauchy equation: x2y" + axy + by = 0 a) Show that y(x)-xrnis a solution where mis equal to m -(1-a) | (1-а)2-b b) Show that for the case when ^1 -a)2 - b 0, the general solution is equal to 4. 4 1-a y(x) = x-2-(G + c2 In x) c) Solve the following problem x2y"-5xy' + 9y-0, y(1)-0.2, y'(1)-0.3 d) Show that for the case when-(1-a)2-b 〈 0, the general solution is equal to 1-а...
Use the reduction of order method to solve the following problem given one of the solution y1. (a) (x^2 - 1)y'' -2xy' +2y = 0 ,y1=x (b) (2x+1)y''-4(x+1)y'+4y=0 ,y1=e^2x (c) (x^2-2x+2)y'' - x^2 y'+x^2 y =0, y1=x (d) Prove that if 1+p+q=0 than y=e^x is a solution of y''+p(x)y'+q(x)y=0, use this fact to solve (x-1)y'' - xy' +y =0
show the ivp is an exact de and then solve (2xy - 9x^2)dx + (2y + x^2 + 1)dy = 0, y(0) = -3
3) Solve the following: max Inx + y x,y ST 2xy 10,x 2 0,y 2 0