What is the solution for (2a^2-r^2)dr=r^3sin(θ)dθ ?

The solution for (2a^2-r^2)dr=r^3sin(θ)dθ is θ(r)=c_{1}+2pin,θ(r)=-c_{1}+2pin

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(2a^2-r^2)dr=r^3sin(θ)dθ

(2 a^{2} - r^{2}) d r = r^{3} sin (θ) d θ

θ (r) = c_{1} + 2 πn, θ (r) = - c_{1} + 2 πn

Solution steps

(2 a^{2} - r^{2}) d r = r^{3} sin (θ (r)) d θ (r)

Solve separable ODE:

θ (r) = c_{1} + 2 πn, θ (r) = - c_{1} + 2 πn

θ (r) = c_{1} + 2 πn, θ (r) = - c_{1} + 2 πn

y^{^{'}} - \frac{y}{x} - 1 = \frac{1}{x} + y

\frac{d y}{d x} = \frac{2 ( y - 1 )}{( x - 1 )}

\frac{d y}{d t} + 2 y = 0, y (0) = 3

\frac{d y}{d x} + 6 x^{2} y = 5 x^{2}, y (0) = 4

y^{^{'}} = x y - 2 x + y - 2

What is the solution for (2a^2-r^2)dr=r^3sin(θ)dθ ?
The solution for (2a^2-r^2)dr=r^3sin(θ)dθ is θ(r)=c_{1}+2pin,θ(r)=-c_{1}+2pin