89.10.10 problem 10

Internal problem ID [24503]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 77
Problem number : 10
Date solved : Thursday, October 02, 2025 at 10:43:26 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (x +2 y+1\right ) y^{\prime }+7+x -4 y&=0 \end{align*}

✓ Maple. Time used: 0.035 (sec). Leaf size: 198

ode:=x-4*y(x)+7+(x+2*y(x)+1)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {4 \left (\left (\frac {i \sqrt {3}}{48}-\frac {1}{48}\right ) \left (12 c_1^{2} \sqrt {3}\, \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_1 -32 x -96}{c_1}}+512+108 \left (x +3\right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{2}/{3}}+\left (\frac {1}{3}+\left (-\frac {x}{4}-1\right ) c_1 \right ) \left (12 c_1^{2} \sqrt {3}\, \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_1 -32 x -96}{c_1}}+512+108 \left (x +3\right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{1}/{3}}+\left (1+i \sqrt {3}\right ) \left (-\frac {4}{3}+\left (x +3\right ) c_1 \right )\right )}{\left (12 c_1^{2} \sqrt {3}\, \left (x +3\right ) \sqrt {\frac {27 \left (x +3\right )^{2} c_1 -32 x -96}{c_1}}+512+108 \left (x +3\right )^{2} c_1^{2}+\left (-576 x -1728\right ) c_1 \right )^{{1}/{3}} c_1} \]

✓ Mathematica. Time used: 60.057 (sec). Leaf size: 2617

ode=( x-4*y[x]+7)+( x+2*y[x]+1 )*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (x + 2*y(x) + 1)*Derivative(y(x), x) - 4*y(x) + 7,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out