69.1.95 problem 142

Internal problem ID [14248]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 142
Date solved : Tuesday, January 28, 2025 at 06:23:18 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

\[ y = {\mathrm e}^{a x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 23

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

\[ y(x)\to e^{a x} (x (c_3 x+c_2)+c_1) \]