29.12.33 problem 352

Internal problem ID [4952]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 352
Date solved : Tuesday, January 28, 2025 at 02:40:36 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{3} y^{\prime }&=\cos \left (y\right ) \left (\cos \left (y\right )-2 x^{2} \sin \left (y\right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.012 (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: 4.357 (sec). Leaf size: 55

DSolve[x^3 D[y[x],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*}