83.33.5 problem 5

Internal problem ID [19413]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (G) at page 115
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:38:48 PM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 39

dsolve(x^2*diff(y(x),x$4)=lambda*diff(y(x),x$2),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +c_{2} x +c_3 \,x^{\frac {5}{2}+\frac {\sqrt {1+4 \lambda }}{2}}+c_4 \,x^{\frac {5}{2}-\frac {\sqrt {1+4 \lambda }}{2}} \]

✓ Solution by Mathematica

Time used: 0.271 (sec). Leaf size: 98

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

\[ y(x)\to \frac {x^{\frac {5}{2}-\frac {1}{2} i \sqrt {-4 \lambda -1}} \left (c_1 \left (\lambda +2 i \sqrt {-4 \lambda -1}+4\right )+c_2 \left (\lambda -2 i \sqrt {-4 \lambda -1}+4\right ) x^{i \sqrt {-4 \lambda -1}}\right )}{(\lambda -6) (\lambda -2)}+c_4 x+c_3 \]