87.8.10 problem 10

Internal problem ID [23364]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 65
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:40:34 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Chini]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 67

ode:=diff(y(x),x)+y(x)^(1/2) = 3*x; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {4 \,\operatorname {arctanh}\left (\sqrt {\frac {y}{x^{2}}}\right )}{5}-\frac {6 \,\operatorname {arctanh}\left (\frac {2 \sqrt {\frac {y}{x^{2}}}}{3}\right )}{5}-\frac {2 \ln \left (-\frac {2 \left (x^{2}-y\right )}{x^{2}}\right )}{5}-\frac {3 \ln \left (-\frac {9 x^{2}-4 y}{3 x^{2}}\right )}{5}-2 \ln \left (x \right )+c_1 = 0 \]

✗ Mathematica

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

Timed out

✗ Sympy

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

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