10.2.17 problem 17

Internal problem ID [1145]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:35:46 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {-{\mathrm e}^{x}+3 x^{2}}{-5+2 y} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.164 (sec). Leaf size: 21

dsolve([diff(y(x),x) = (-exp(x)+3*x^2)/(-5+2*y(x)),y(0) = 1],y(x), singsol=all)
 

\[ y = \frac {5}{2}-\frac {\sqrt {13+4 x^{3}-4 \,{\mathrm e}^{x}}}{2} \]

✓ Solution by Mathematica

Time used: 0.798 (sec). Leaf size: 29

DSolve[{D[y[x],x] == (-Exp[x]+3*x^2)/(-5+2*y[x]),y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (5-\sqrt {4 x^3-4 e^x+13}\right ) \]