en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2y^{''}=2xy^'+(y^')^2

Solution

x^{2} y^{^{''}} = 2 x y^{^{'}} + (y^{^{'}})^{2}

Solution

y = - \frac{1}{2} x^{2} - c_{1} x - c_{1}^{2} ln (- x + c_{1}) + \frac{3}{2} c_{1}^{2} + c_{2}

Solution steps

x^{2} y^{''} (x) = 2 x y^{'} (x) + (y^{'} (x))^{2}

Solve using substitution:

y = - \frac{1}{2} x^{2} - c_{1} x - c_{1}^{2} ln (- x + c_{1}) + \frac{3}{2} c_{1}^{2} + c_{2}

y = - \frac{1}{2} x^{2} - c_{1} x - c_{1}^{2} ln (- x + c_{1}) + \frac{3}{2} c_{1}^{2} + c_{2}

Popular Examples

tangent of f(x)=x^2+8,(1,9)tangent of

f (x) = x^{2} + 8, (1, 9)

derivative of (4x^3/(x^4+27))

\frac{d}{d x} (\frac{4 x ^{3}}{x ^{4} + 27})

derivative of arcsin(tan(sqrt(x^2+1)))

\frac{d}{d x} (arcsin (tan (x^{2} + 1)))

(\partial)/(\partial x)(ln(x^8y))

\frac{\partial}{\partial x} (ln (x^{8} y))

limit as x approaches 0 of-1/(x^2)

x \to 0 lim (- \frac{1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the solution for x^2y^{''}=2xy^'+(y^')^2 ?
The solution for x^2y^{''}=2xy^'+(y^')^2 is y=-1/2 x^2-c_{1}x-c_{1}^2ln(-x+c_{1})+3/2 c_{1}^2+c_{2}