29.7.24 problem 199

Internal problem ID [4799]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 199
Date solved : Monday, January 27, 2025 at 09:39:47 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x y^{\prime }+\left (\sin \left (y\right )-3 x^{2} \cos \left (y\right )\right ) \cos \left (y\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)+(sin(y(x))-3*x^2*cos(y(x)))*cos(y(x)) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \arctan \left (\frac {x^{3}+2 c_{1}}{x}\right ) \]

✓ Solution by Mathematica

Time used: 1.923 (sec). Leaf size: 53

DSolve[x D[y[x],x]+(Sin[y[x]]-3 x^2 Cos[y[x]]) Cos[y[x]]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \arctan \left (x^2+\frac {c_1}{2 x}\right ) \\ y(x)\to -\frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ y(x)\to \frac {1}{2} \pi \sqrt {\frac {1}{x^2}} x \\ \end{align*}