DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS

Due the 17th of September 1. Find the values of the parameter r for which y = erx is a solution of

the equation y′′ + 2y′ −15y = 0.

2. . Find the values of the parameter r for which y = erx is a solution of the equation

y′′ + 6y′ −7y = 0. 3. Find the solution of the differential equation

y′ = 2x

1 + x2 ,

such that y(0) = 0. 4. Find the solution of the differential equation

y′ = esin x cosx,

such that y(0) = 1. 5. Find the general solution of the differential equation

2y′ + exy3 = 0.

6. Find the general solution of the differential equation

y′ = 2xex 2−y.

7. Find the general solution of the differential equation

y′ = ex √

1−y2. 8. Find the solution of the differential equation

y′ = 5 + 2x + 5y + 2xy,

such that y(0) = 0. 9. Find the solution of the differential equation

(1 + sin(x4))y′ + 4x3 cos(x4)y = 2x,

such that y(0) = 0. 10. Find the solution of the differential equation

(1 + x4)y′ + 4x3 y = ex,

such that y(0) = 1. 1

2 DIFFERENTIAL EQUATIONS

11. Find the general solution of the equation

y′ = xy + 2y2 + 2x2

x2

in the region {(x,y) ∈ R2 : x > 0}. 12. Find the general solution of the equation

y′ = e−y/x + y/x

in the region {(x,y) ∈ R2 : x > 0}. 13. Apply Euler’s method with the step h = 1/2 to find an approximation

of y(1), where y is the solution of the initial value problem

y′ = 1 + 4y2, y(0) = 0.

14. Apply Euler’s method with the step h = 1/2 to find an approximation of y(1), where y is the solution of the initial value problem

y′ = sin(πxy), y(0) = 1.

15. Apply Euler’s method with the step h = 1/2 to find an approximation of y(1), where y is the solution of the initial value problem

y′ = 2x2y, y(0) = 1.