82.41.2 problem Ex. 3

Internal problem ID [18955]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 96
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:38:20 PM
CAS classification : [[_high_order, _quadrature]]

\begin{align*} x^{2} y^{\prime \prime \prime \prime }+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(x^2*diff(y(x),x$4)+1=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\ln \left (x \right ) x^{2}}{2}+\frac {c_{1} x^{3}}{6}+\frac {\left (-3+2 c_{2} \right ) x^{2}}{4}+c_3 x +c_4 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 37

DSolve[x^2*D[y[x],{x,4}]+1==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_4 x^3+\frac {1}{2} x^2 \log (x)+\left (-\frac {3}{4}+c_3\right ) x^2+c_2 x+c_1 \]