29.5.22 problem 139

Internal problem ID [4739]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 5
Problem number : 139
Date solved : Monday, January 27, 2025 at 09:34:58 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

dsolve(2*diff(y(x),x) = 2*sin(y(x))^2*tan(y(x))-x*sin(2*y(x)),y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 7.875 (sec). Leaf size: 66

DSolve[2 D[y[x],x]==2 Sin[y[x]]^2 Tan[y[x]]- x Sin[2 y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right ) \\ y(x)\to \cot ^{-1}\left (\sqrt {e^{x^2} \left (-\sqrt {\pi } \text {erf}(x)+4 c_1\right )}\right ) \\ y(x)\to 0 \\ \end{align*}