83.30.5 problem 5

Internal problem ID [19384]
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 (D) at page 109
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:36:28 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }-4 x y^{\prime \prime }+6 y^{\prime }&=4 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(x^2*diff(y(x),x$3)-4*x*diff(y(x),x$2)+6*diff(y(x),x)=4,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.012 (sec). Leaf size: 31

DSolve[x^2*D[y[x],{x,3}]-4*x*D[y[x],{x,2}]+6*D[y[x],x]==4,y[x],x,IncludeSingularSolutions -> True]
 

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