83.8.31 problem 32

Internal problem ID [19157]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Misc examples on chapter II at page 25
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 01:10:32 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Solution by Maple

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

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 18.467 (sec). Leaf size: 105

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

\begin{align*} y(x)\to \arctan \left (\frac {1}{2} \left (x^2-8 c_1 e^{-x^2}-1\right )\right ) \\ y(x)\to -\arctan \left (-\frac {x^2}{2}+4 c_1 e^{-x^2}+\frac {1}{2}\right ) \\ y(x)\to -\frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ y(x)\to \frac {1}{2} \pi e^{x^2} \sqrt {e^{-2 x^2}} \\ \end{align*}