83.25.4 problem 4

Internal problem ID [19324]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VI. Homogeneous linear equations with variable coefficients. Exercise VI (B) at page 83
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:34:09 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }+3 x y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 16

dsolve(x^2*diff(y(x),x$3)+3*x*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +\sin \left (\ln \left (x \right )\right ) c_{2} +c_3 \cos \left (\ln \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,3}]+3*x*D[y[x],{x,2}]+2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -c_1 \cos (\log (x))+c_2 \sin (\log (x))+c_3 \]