83.43.14 problem Ex 15 page 15

Internal problem ID [19522]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter II. Equations of first order and first degree
Problem number : Ex 15 page 15
Date solved : Tuesday, January 28, 2025 at 08:32:49 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 18.565 (sec). Leaf size: 105

DSolve[D[y[x],x]+x*Sin[2*y[x]]==x^3*Cos[y[x]]^2,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*}