Internal problem ID [3668]
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]
\[ \boxed {\left (\operatorname {a0} +\operatorname {a1} \sin \left (x \right )^{2}\right ) y^{\prime }+\operatorname {a1} y \sin \left (2 x \right )=-\operatorname {a2} x \left (\operatorname {a3} +\operatorname {a1} \sin \left (x \right )^{2}\right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 53
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)
\[ y \left (x \right ) = \frac {\operatorname {a2} \left (\frac {\operatorname {a1} \left (\cos \left (2 x \right )+2 x \sin \left (2 x \right )\right )}{4}-\frac {\operatorname {a1} \,x^{2}}{2}-\operatorname {a3} \,x^{2}\right )+2 c_{1}}{-\operatorname {a1} \cos \left (2 x \right )+2 \operatorname {a0} +\operatorname {a1}} \]
✓ Solution by Mathematica
Time used: 0.411 (sec). Leaf size: 58
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]
\[ y(x)\to \frac {-2 \text {a1} \text {a2} x^2+2 \text {a1} \text {a2} x \sin (2 x)+\text {a1} \text {a2} \cos (2 x)-4 \text {a2} \text {a3} x^2+4 c_1}{4 (2 \text {a0}-\text {a1} \cos (2 x)+\text {a1})} \]