70.1.23 problem 23

Internal problem ID [18609]
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 : Thursday, October 02, 2025 at 03:16:07 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.272 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.568 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{2} \left (\sqrt {4 x^3-4 e^x+125}+11\right ) \end{align*}

✓ Sympy. Time used: 0.381 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x**2 + exp(x))/(2*y(x) - 11) + Derivative(y(x), x),0) 
ics = {y(0): 11} 
dsolve(ode,func=y(x),ics=ics)
 

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