57.1.68 problem 68

Internal problem ID [9052]
Book : First order enumerated odes
Section : section 1
Problem number : 68
Date solved : Monday, January 27, 2025 at 05:31:34 PM
CAS classification : [[_1st_order, `_with_symmetry_[F(x),G(x)]`]]

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 30

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

\[ y = \frac {x^{3}}{3}-\ln \left (-c_{1} -10 \left (\int {\mathrm e}^{\frac {x \left (x^{2}+3\right )}{3}}d x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.437 (sec). Leaf size: 115

DSolve[D[y[x],x]==10*Exp[x+y[x]]+x^2,y[x],x,IncludeSingularSolutions -> True]
 

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