4.2.17 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 : Tuesday, September 30, 2025 at 04:23:46 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*}

✓ Maple. Time used: 0.186 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.574 (sec). Leaf size: 29

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

\begin{align*} y(x)&\to \frac {1}{2} \left (5-\sqrt {4 x^3-4 e^x+13}\right ) \end{align*}

✓ Sympy. Time used: 0.507 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x**2 + exp(x))/(2*y(x) - 5) + Derivative(y(x), x),0) 
ics = {y(0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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