Differential Equations Answers

Solve:(𝐷2 −2𝐷𝐷′ +𝐷′2)𝑍=𝑥2𝑦2𝑒𝑥+𝑦

Y"+6y'+9y=-xe^4x by variation of parameters

For any X and suitable p and q, solve y=Xp^qz for z

*** Y=Xp^q to the power z

Solve the following equation of first order but not of first degree y=2xp-p²

Solve dx/x(x+y) = dy/-y(x+y) = dz/-(x-y)(2x+2y+z)

 Solve the equation of the Linear Homogeneous Differential Equations with Constant 

Coefficients.

1. Solve y’’ – y’ – 2y = 0

2. Solve y’’ + 4y = 0

3. (D3 + 3D2 – 4D)y = 0

4. (D2 – 6D + 9)y = 0

.(6𝑥2 −𝑦+3)𝑑𝑥+(3𝑦2 −𝑥−2)𝑑𝑦=0

X3+x2y-xy2+y3/x2y+xy2

whetther homogeneous or not by dx/dy

Solve the boundary value problem

y''-y=0

With boundary condition

y(0)=0, y(2)=3.6268

Do the functions 

y1(t)=√t and y2(t)=1/t

form a fundamental set of solutions of the 

equation 2t²y"+3ty'-y=0

, on the interval 

0 < t <infinity

Justify your answer.