60.4.72 problem 1522

Internal problem ID [11523]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1522
Date solved : Monday, January 27, 2025 at 11:23:10 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} 4 x^{4} y^{\prime \prime \prime }-4 x^{3} y^{\prime \prime }+4 x^{2} y^{\prime }-1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

dsolve(4*x^4*diff(diff(diff(y(x),x),x),x)-4*x^3*diff(diff(y(x),x),x)+4*x^2*diff(y(x),x)-1=0,y(x), singsol=all)
 

\[ y = \frac {18 x^{3} c_{1} \ln \left (x \right )-1+\left (-9 c_{1} +18 c_{2} \right ) x^{3}+36 x c_3}{36 x} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 42

DSolve[-1 + 4*x^2*D[y[x],x] - 4*x^3*D[y[x],{x,2}] + 4*x^4*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} (2 c_1-c_2) x^2+\frac {1}{2} c_2 x^2 \log (x)-\frac {1}{36 x}+c_3 \]