75.19.9 problem 626

Internal problem ID [17125]
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 : 626
Date solved : Tuesday, January 28, 2025 at 09:53:39 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (1+x \right )^{2} y^{\prime \prime \prime }-12 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve((x+1)^2*diff(y(x),x$3)-12*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\left (x +1\right )^{5} c_{2} +\frac {c_{3}}{\left (x +1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 30

DSolve[(x+1)^2*D[y[x],{x,3}]-12*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{5} c_1 (x+1)^5-\frac {c_2}{2 (x+1)^2}+c_3 \]