56.3.29 problem 29

Internal problem ID [8887]
Book : Own collection of miscellaneous problems
Section : section 3.0
Problem number : 29
Date solved : Monday, January 27, 2025 at 05:18:32 PM
CAS classification : [[_homogeneous, `class D`]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 18

dsolve(diff(y(x),x)= 2*x^2 * sin(y(x)/x)^2 + y(x)/x,y(x), singsol=all)
 

\[ y = \left (\frac {\pi }{2}+\arctan \left (x^{2}+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 22

DSolve[D[y[x],x]== 2*x^2 * Sin[y[x]/x]^2 + y[x]/x,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -x \cot ^{-1}\left (x^2-2 c_1\right ) \\ y(x)\to 0 \\ \end{align*}