15.14.21 problem 21

Internal problem ID [3193]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 21
Date solved : Monday, January 27, 2025 at 07:25:50 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 35

dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+diff(y(x),x$2)=x^2,y(x), singsol=all)
 

\[ y = \left (c_{1} x +c_2 -2 c_{1} \right ) {\mathrm e}^{x}+\frac {x^{4}}{12}+\frac {2 x^{3}}{3}+3 x^{2}+x c_3 +c_4 \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 46

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,3}]+D[y[x],{x,2}]==x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {x^4}{12}+\frac {2 x^3}{3}+3 x^2+c_4 x+c_1 e^x+c_2 e^x (x-2)+c_3 \]