Differential Equations Answers

𝑦(2𝑥𝑦 + 1)𝑑𝑥 − 𝑥𝑑𝑦 = 0

Find the general solution of the following

2x²y^''-xy^'+(x-5)y=0

Find the Taylor series solution of following

(X²+1)y^''+4xy^'+(x-5)y=0 y(2)=-1

y^'(2)=3

Use the Taylor series expansion to find the general solution of each of the following

2x²y''-3xy'+(x+1)y=0

y(1)=4 y^'(1)=1

Solve the following system of equations

dx/dt-dy/dt-2x-4y=t²

dx/dt+dy/dt-x-y=1

Solve the following systems of equations

2dx/dt+dy/dt-3x-y=t

dx/dt+dy/dt-4x-y=e^t

Solve the following differential equation

dx/dt+dy/dt-2x-4y=e^t

dx/dt+dy/dt-y=e^4t

solve problem 23 under the assumption that the solution is pumped out at a faster rate of 10 gal/min when is the tank empty

solve(d^2+dd'-6d'^2)z=cos(2x+y)

Show by the method of variation of parameters that the general solution of the differential equation -y^''=f(x) can be written in the form y = φ ( x) = c₁+c₂x-∫₀^x(x-s)f(s)ds where c₁ and c₂ are arbitrary constants.