40.14.4 problem 25

Internal problem ID [6775]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:30:15 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 28

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

\[ y = \frac {x^{4}}{12}+x^{2}-\frac {x^{3}}{3}+c_1 \,{\mathrm e}^{-x}+c_2 x +c_3 \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 37

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

\[ y(x)\to \frac {x^4}{12}-\frac {x^3}{3}+x^2+c_3 x+c_1 e^{-x}+c_2 \]