Internal problem ID [3608]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 12
Problem number: 352.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {x^{3} y^{\prime }-\cos \left (y\right ) \left (\cos \left (y\right )-2 \sin \left (y\right ) x^{2}\right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(x^3*diff(y(x),x) = cos(y(x))*(cos(y(x))-2*x^2*sin(y(x))),y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (\frac {\ln \left (x \right )-c_{1}}{x^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 5.952 (sec). Leaf size: 55
DSolve[x^3 y'[x]==Cos[y[x]](Cos[y[x]]-2 x^2 Sin[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arctan \left (\frac {\log (x)+4 c_1}{x^2}\right ) y(x)\to -\frac {1}{2} \pi \sqrt {\frac {1}{x^4}} x^2 y(x)\to \frac {1}{2} \pi \sqrt {\frac {1}{x^4}} x^2 \end{align*}