12.5.6 problem 2

Internal problem ID [1630]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Transformation of Nonlinear Equations into Separable Equations. Section 2.4 Page 68
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:15:16 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} 7 x y^{\prime }-2 y&=-\frac {x^{2}}{y^{6}} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 134

dsolve(7*x*diff(y(x),x)-2*y(x)=-x^2/y(x)^6,y(x), singsol=all)
 

\begin{align*} y &= \left (-x^{2} \left (\ln \left (x \right )-c_1 \right )\right )^{{1}/{7}} \\ y &= -\left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{1}/{7}} \\ y &= \left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{6}/{7}} \\ y &= -\left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{5}/{7}} \\ y &= \left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{2}/{7}} \\ y &= -\left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{3}/{7}} \\ y &= \left (\left (c_1 -\ln \left (x \right )\right ) x^{2}\right )^{{1}/{7}} \left (-1\right )^{{4}/{7}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.223 (sec). Leaf size: 181

DSolve[7*x*D[y[x],x]-2*y[x]==-x^2/y[x]^6,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -\sqrt [7]{-1} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{2/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -(-1)^{3/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{4/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to -(-1)^{5/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ y(x)\to (-1)^{6/7} x^{2/7} \sqrt [7]{-\log (x)+c_1} \\ \end{align*}