51.1.68 problem 68

Internal problem ID [10338]
Book : First order enumerated odes
Section : section 1
Problem number : 68
Date solved : Tuesday, September 30, 2025 at 07:22:17 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

\begin{align*} y^{\prime }&=10 \,{\mathrm e}^{x +y}+x^{2} \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 30

ode:=diff(y(x),x) = 10*exp(x+y(x))+x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x^{3}}{3}-\ln \left (-c_1 -10 \int {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}d x \right ) \]

✓ Mathematica. Time used: 0.253 (sec). Leaf size: 115

ode=D[y[x],x]==10*Exp[x+y[x]]+x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{y(x)}-\frac {1}{10} e^{-K[2]} \left (10 e^{K[2]} \int _1^x-\frac {1}{10} e^{\frac {K[1]^3}{3}-K[2]} K[1]^2dK[1]+e^{\frac {x^3}{3}}\right )dK[2]+\int _1^x\left (\frac {1}{10} e^{\frac {K[1]^3}{3}-y(x)} K[1]^2+e^{\frac {K[1]^3}{3}+K[1]}\right )dK[1]=c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.963 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - 10*exp(x + y(x)) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \log {\left (\frac {\sqrt [3]{e^{x^{3}}}}{C_{1} - 10 \int e^{x} \sqrt [3]{e^{x^{3}}}\, dx} \right )} \]