29.10.10 problem 276

Internal problem ID [4876]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 276
Date solved : Tuesday, January 28, 2025 at 02:40:00 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2} y^{\prime }&=\sec \left (y\right )+3 x \tan \left (y\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 17

dsolve(x^2*diff(y(x),x) = sec(y(x))+3*x*tan(y(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \arcsin \left (\frac {c_{1} x^{4}-1}{4 x}\right ) \]

✓ Solution by Mathematica

Time used: 9.362 (sec). Leaf size: 23

DSolve[x^2 D[y[x],x]==Sec[y[x]]+3 x Tan[y[x]],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\arcsin \left (\frac {1}{4 x}+3 c_1 x^3\right ) \]