54.4.59 problem 1517

Internal problem ID [12781]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1517
Date solved : Wednesday, October 01, 2025 at 02:21:48 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{3} y^{\prime \prime \prime }+x^{2} y^{\prime \prime }+\ln \left (x \right )+2 x y^{\prime }-y-2 x^{3}&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 1195

ode:=x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)+ln(x)+2*x*diff(y(x),x)-y(x)-2*x^3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {Expression too large to display} \]

✓ Mathematica. Time used: 0.227 (sec). Leaf size: 762

ode=-2*x^3 + Log[x] - y[x] + 2*x*D[y[x],x] + x^2*D[y[x],{x,2}] + x^3*Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 0.862 (sec). Leaf size: 246

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

\[ y{\left (x \right )} = C_{1} x^{- \frac {2^{\frac {2}{3}} \sqrt [3]{11 + 3 \sqrt {69}}}{6} + \frac {5 \sqrt [3]{2}}{3 \sqrt [3]{11 + 3 \sqrt {69}}} + \frac {2}{3}} + C_{2} x^{- \frac {5 \sqrt [3]{2}}{6 \sqrt [3]{11 + 3 \sqrt {69}}} + \frac {2^{\frac {2}{3}} \sqrt [3]{11 + 3 \sqrt {69}}}{12} + \frac {2}{3}} \sin {\left (\frac {\sqrt [3]{2} \sqrt {3} \left (\frac {10}{\sqrt [3]{11 + 3 \sqrt {69}}} + \sqrt [3]{2} \sqrt [3]{11 + 3 \sqrt {69}}\right ) \log {\left (x \right )}}{12} \right )} + C_{3} x^{- \frac {5 \sqrt [3]{2}}{6 \sqrt [3]{11 + 3 \sqrt {69}}} + \frac {2^{\frac {2}{3}} \sqrt [3]{11 + 3 \sqrt {69}}}{12} + \frac {2}{3}} \cos {\left (\frac {\sqrt [3]{2} \sqrt {3} \left (\frac {10}{\sqrt [3]{11 + 3 \sqrt {69}}} + \sqrt [3]{2} \sqrt [3]{11 + 3 \sqrt {69}}\right ) \log {\left (x \right )}}{12} \right )} + \frac {2 x^{3}}{17} + \log {\left (x \right )} + 3 \]