76.1.23 problem 23

Internal problem ID [17322]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 23
Date solved : Tuesday, January 28, 2025 at 10:00:11 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}-{\mathrm e}^{x}}{2 y-11} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=11 \end{align*}

✓ Solution by Maple

Time used: 0.215 (sec). Leaf size: 21

dsolve([diff(y(x),x)=(3*x^2-exp(x))/(2*y(x)-11),y(0) = 11],y(x), singsol=all)
 

\[ y = \frac {11}{2}+\frac {\sqrt {125+4 x^{3}-4 \,{\mathrm e}^{x}}}{2} \]

✓ Solution by Mathematica

Time used: 0.853 (sec). Leaf size: 27

DSolve[{D[y[x],x]==(3*x^2-Exp[x])/(2*y[x]-11),{y[0]==11}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (\sqrt {4 x^3-4 e^x+125}+11\right ) \]