Internal problem ID [12512]
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.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = {\mathrm e}^{a x} \left (c_{3} x^{2}+c_{2} x +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 23
DSolve[y'''[x]-3*a*y''[x]+3*a^2*y'[x]-a^3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{a x} (x (c_3 x+c_2)+c_1) \]