Question

Find the general solution of the given differential equation: d²r/dr²(θ) = cos(θ)

Answer 1

To find the general solution of the given differential equation: d²r/dr²(θ) = cos(θ), integrate twice with respect to θ to get the general solution rθ = -cos(θ) + C₁θ + C₂.

Step-by-step explanation:

To find the general solution of the given differential equation: d²r/dr²(θ) = cos(θ), we can integrate twice.

First, integrate the equation with respect to θ to get: dr/dr = ∫cos(θ) dθ

Simplifying the integral gives: r = sin(θ) + C₁

Next, integrate again with respect to θ to get: ∫dr = ∫(sin(θ) + C₁) dθ

Simplifying the integral gives: rθ = -cos(θ) + C₁θ + C₂

So, the general solution to the differential equation is given by: rθ = -cos(θ) + C₁θ + C₂