75.19.7 problem 624

Internal problem ID [17123]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 624
Date solved : Tuesday, January 28, 2025 at 09:53:38 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }-3 x y^{\prime \prime }+3 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

dsolve(x^2*diff(y(x),x$3)-3*x*diff(y(x),x$2)+3*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{3} x^{4}+c_{2} x^{2}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 26

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

\[ y(x)\to \frac {c_2 x^4}{4}+\frac {c_1 x^2}{2}+c_3 \]