77.8.16 problem 17

Internal problem ID [20427]
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 : Thursday, October 02, 2025 at 05:58:40 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

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

\[ y = \frac {\ln \left (2\right )}{2}-\frac {\ln \left (3\right )}{2}+\frac {\ln \left (x^{3}+{\mathrm e}^{3 x}+3 c_1 \right )}{2} \]

✓ Mathematica. Time used: 1.0 (sec). Leaf size: 27

ode=D[y[x],x]==Exp[3*x-2*y[x]]+x^2*Exp[-2*y[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} \log \left (\frac {2}{3} \left (x^3+e^{3 x}+3 c_1\right )\right ) \end{align*}

✓ Sympy. Time used: 0.459 (sec). Leaf size: 48

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*exp(-2*y(x)) - exp(3*x - 2*y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = \log {\left (- \sqrt {C_{1} + 6 x^{3} + 6 e^{3 x}} \right )} - \log {\left (3 \right )}, \ y{\left (x \right )} = \frac {\log {\left (C_{1} + 6 x^{3} + 6 e^{3 x} \right )}}{2} - \log {\left (3 \right )}\right ] \]