Differential Equations Answers

Solve

x ^ 2 * (d ^ 2 * y)/(d * x ^ 2) - 2x * (dy)/(dx) - 4y = x ^ 2 + 2 * log x

Solve

x ^ 2 * (d ^ 2 * y)/(dx) + x * (dy)/(dx) - 9y = 48x ^ 5

An inductor of 2 henries, resistor of 16 ohms and capacitor of 0.02 farads are connected in series with a battery of

e.m.f E = 100sin33t. At t=0, the charge on the capacitor and current in the circuit are zero. Find the charge and

current at time t.

Find the isogonal trajectories of the family of curves x²+y²=c if θ=45°.

Which of the following ODE is linear or non-linear, also show their orders of degree

• (dL/dm)²+2mL²=10
• (d²y/dx²)^5/3+(dy/dx)⁹+10=0

Solve the ODE xe^x2+ydx=ydy

1. A certain planet has an average surface area that is 2.25% larger than the earth and a gravitational acceleration that is three fifth times than that of the earth’s gravitational acceleration. What is the velocity of escape on that planet? Ans. 8728.33 m/s
2. Find the isogonal trajectories of the family of curves x²+y²=c if θ=45°. Ans. ln(x²+y²)+2 arctan (x/y) =k

xdy/dx+ (x+1) y = x³

xdy/dx + (x+1) y = x³

Find the integrating factor to transform the given differential equation into the equation in exact differentials: (x²-3y²)dx+2xydy=0 μ=μ(x)