Differential Equations Answers

F or the follow ing differential equation locate and classify its singular points on the x-axis

𝑥

2

𝑦

′′ + (2 − 𝑥 )𝑦

′ = 0.

S how that y = c 1

e

x + c 2

e

2 x

is the general solution of y

′′ − 3 y

′ + 2y = 0 on any

interval, and find the particular solution for w hich y 0 = − 1 a n d y

′

( 0) = 1.

Solve the initial value problem (IVP):

(D^2+4D+4)=9e^x

y(0)=2

y'(0)=1

Solve the partial differential equation (3D² +10DD'+ 3D ^1^2)z^ =e^x-y

y’’’’-5y’’’+6y’’+4y’-8y=0

(D ^ 2 + 3D + 2) * y = sin 2x + 5 degrees + log 3

Find a complete integral of x(1 + y)p = y(1 + x)q

If a string of length l is initially at rest in equilibrium position and each of its points is given the velocity dy/dt= b sin^3πx/l find the displacement