Internal problem ID [3160]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 15
Problem number: 414.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\left (\mathit {a0} +\mathit {a1} \left (\sin ^{2}\relax (x )\right )\right ) y^{\prime }+\mathit {a2} x \left (\mathit {a3} +\mathit {a1} \left (\sin ^{2}\relax (x )\right )\right )+\mathit {a1} y \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 56
dsolve((a0+a1*sin(x)^2)*diff(y(x),x)+a2*x*(a3+a1*sin(x)^2)+a1*y(x)*sin(2*x) = 0,y(x), singsol=all)
\[ y \relax (x ) = \frac {-2 \mathit {a2} x \mathit {a1} \sin \left (2 x \right )+2 \mathit {a2} \mathit {a1} \,x^{2}+4 \mathit {a2} \mathit {a3} \,x^{2}-\mathit {a2} \mathit {a1} \cos \left (2 x \right )-8 c_{1}}{4 \mathit {a1} \cos \left (2 x \right )-8 \mathit {a0} -4 \mathit {a1}} \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 54
DSolve[(a0+a1 Sin[x]^2)y'[x]+a2 x(a3+a1 Sin[x]^2)+a1 y[x] Sin[2 x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 \text {a2} x^2 (\text {a1}+2 \text {a3})+\text {a1} \text {a2} (2 x \sin (2 x)+\cos (2 x))+4 c_1}{4 (2 \text {a0}-\text {a1} \cos (2 x)+\text {a1})} \\ \end{align*}