83.3.2 problem 2

Internal problem ID [19058]
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. Exercise II (B) at page 9
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 12:49:42 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 21

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

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

✓ Solution by Mathematica

Time used: 1.077 (sec). Leaf size: 19

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

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