83.3.6 problem 6

Internal problem ID [19062]
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 : 6
Date solved : Tuesday, January 28, 2025 at 12:49:50 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 1.053 (sec). Leaf size: 25

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

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