44.3.14 problem 22

Internal problem ID [6995]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 22
Date solved : Sunday, March 30, 2025 at 11:33:23 AM
CAS classification : [_Chini]

\begin{align*} y^{\prime }&=6 \sqrt {y}+5 x^{3} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=4 \end{align*}

✗ Maple

ode:=diff(y(x),x) = 6*y(x)^(1/2)+5*x^3; 
ic:=y(-1) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==6*Sqrt[y[x]]+5*x^3; 
ic={y[-1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-5*x**3 - 6*sqrt(y(x)) + Derivative(y(x), x),0) 
ics = {y(-1): 4} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -5*x**3 - 6*sqrt(y(x)) + Derivative(y(x), x) cannot be solved by the lie group method