83.48.19 problem Ex 19 page 114

Internal problem ID [19611]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 19 page 114
Date solved : Tuesday, January 28, 2025 at 02:04:30 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

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

\[ y \left (x \right ) = c_{1} +c_{2} x +c_3 \,{\mathrm e}^{a x}+c_4 \,{\mathrm e}^{-a x} \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 34

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

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