29.26.18 problem 754
Internal
problem
ID
[5339]
Book
:
Ordinary
differential
equations
and
their
solutions.
By
George
Moseley
Murphy.
1960
Section
:
Various
26
Problem
number
:
754
Date
solved
:
Tuesday, March 04, 2025 at 09:29:43 PM
CAS
classification
:
[[_homogeneous, `class G`]]
\begin{align*} {y^{\prime }}^{2}+a \,x^{2}+b y&=0 \end{align*}
✗ Maple
ode:=diff(y(x),x)^2+a*x^2+b*y(x) = 0;
dsolve(ode,y(x), singsol=all);
\[ \text {No solution found} \]
✓ Mathematica. Time used: 1.51 (sec). Leaf size: 581
ode=(D[y[x],x])^2+a x^2+b*y[x]==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4-\text {$\#$1}^3 b+2 \text {$\#$1}^2 a+\text {$\#$1} a b+a^2\&,\frac {2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )-2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+\text {$\#$1}^2 b \log (x)+2 \text {$\#$1} a \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )-2 \text {$\#$1} a \log (x)-a b \log (x)}{4 \text {$\#$1}^3-3 \text {$\#$1}^2 b+4 \text {$\#$1} a+a b}\&\right ]-\log \left (\sqrt {-b y(x)} \sqrt {-a x^2-b y(x)}+b y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\
\text {Solve}\left [\text {RootSum}\left [\text {$\#$1}^4+\text {$\#$1}^3 b+2 \text {$\#$1}^2 a-\text {$\#$1} a b+a^2\&,\frac {-2 \text {$\#$1}^3 \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+2 \text {$\#$1}^3 \log (x)-\text {$\#$1}^2 b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+\text {$\#$1}^2 b \log (x)-2 \text {$\#$1} a \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+a b \log \left (\text {$\#$1} x-\sqrt {-a x^2-b y(x)}+\sqrt {-b y(x)}\right )+2 \text {$\#$1} a \log (x)-a b \log (x)}{-4 \text {$\#$1}^3-3 \text {$\#$1}^2 b-4 \text {$\#$1} a+a b}\&\right ]-\log \left (\sqrt {-b y(x)} \sqrt {-a x^2-b y(x)}+b y(x)\right )+\frac {1}{2} \log (y(x))+2 \log (x)&=c_1,y(x)\right ] \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
a = symbols("a")
b = symbols("b")
y = Function("y")
ode = Eq(a*x**2 + b*y(x) + Derivative(y(x), x)**2,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
NotImplementedError : The given ODE -sqrt(-a*x**2 - b*y(x)) + Derivative(y(x), x) cannot be solved by the factorable group method