83.8.16 problem 17

Internal problem ID [19142]
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 : 17
Date solved : Tuesday, January 28, 2025 at 01:05:19 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&={\mathrm e}^{3 x -2 y}+x^{2} {\mathrm e}^{-2 y} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 27

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

\[ y \left (x \right ) = \frac {\ln \left (2\right )}{2}-\frac {\ln \left (3\right )}{2}+\frac {\ln \left (x^{3}+{\mathrm e}^{3 x}+3 c_{1} \right )}{2} \]

✓ Solution by Mathematica

Time used: 1.200 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{2} \log \left (\frac {2}{3} \left (x^3+e^{3 x}+3 c_1\right )\right ) \]