3. Verify that y1(x) x is a solution of Find the general solution of the DE...
consider the Riccati equation y'=p(x)+q(x)y+r(x)y^2. If a particular solution y1(x), show that the general solution y(x) has the from y(x)=y1(x)+z(x); where z(x) is the solution of the bernoulli equation: z'-(q+zry1)z=rz^2 Use this technique to find the general solution of the equation, y'=y/x+x^3y^2-x^5. (Hint: Verify that y1(x)=x is a particular solution)
Verify that the given functions Y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. x2y" – 3xy' + 4y = 7x? In x, x>0; 71(x) = x2, yz(x) = x2 In x Y(x) =
1 -2 Find the general solution to the homogeneous system of DE: 3 2 6 x' = Ax where A = -2 1 -2
Find the general solution to the non-homogeneous system of DE: -4 51 3t X + -4 0 x'
Find the general solution to the non-homogeneous system of DE: -4 X+
3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial
3. Find the general solution of the given differential equation: (15 points) Hint: verify if m-l is a root of the auxiliary polynomial
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
Find the general solution of the DE:
y’’(x) + 6y’(x) + 8y(x) = 3e^(-2x) + 2x
given y1=x is a solution of the following DEXX+2xy-2y=0, the second solution is x 2 e2 Question 2 2 pts The differential equation whose general solution is Y=CCos(6x)+C2 Sin (V6 x) y" by 0 Oy -6y=0 y +6y=0 y"+6y'=0 2 pts Question 3 given that y1= x1 is a solution, if we use the reduction of order to solve the ODE 2x2 y + xy - 3y=0 we find that u= AXR+B (Ax512 - Ax+B Axe5124B
2 8. (10 points) Find the general solution to the homogeneous system of DE: | 3 x' = Ax where A = -2 1 - 1 -2 -4.