Form the differential equation by eliminating α and β from (x − α)² + (y − β)² = r²

Find the differential equation of the family of all straight lines passing through the origin.

Solve the following differential equations (D²+D−6)y=e^3x + e^−3x

Solve the following differential equations (D²−10D+25)y = 4e^5x + 5

Solve (D²- 3D + 2)y = e^4x given y = 0 when x = 0 and x = 1.

Find the order and degree of the following differential equations.
\(\frac { d^{ 2 }y }{ { dx }^{ 2 } } =\sqrt { y-\frac { dy }{ dx } } \)

Find the order and degree of the following differential equations.
\({ \left( \frac { dy }{ dx } \right) }^{ 3 }+y=x-\frac { dx }{ dy } \)

Solve: \(\frac { 1+{ x }^{ 2 } }{ 1+y } =xy\frac { dy }{ dx } \)

Solve: \(\frac { dy }{ dx } \) + e^x+ye^x = 0

Write down the order and degree of the following differential equations.
\(\left( \frac { dy }{ dx } \right) ^{ 2 }-7\frac { d^{ 3 }y }{ { dx }^{ 3 } } +y\frac { { d }^{ 2 }y }{ dx^{ 2 } } +4\frac { dy }{ dx } \)- log x = 0

Write down the order and degree of the following differential equations.
\(\left[ 1+\left( \frac { dy }{ dx } \right) ^{ 2 } \right] ^{ \frac { 2 }{ 3 } }=\frac { d^{ 2 }y }{ { dx }^{ 2 } } \)

Find the differential equation for y = mx + \(\frac { a }{ m } \) where m is arbitrary constant.

Solve: x dy +y dx = 0

The change in the cost of ordering and holding C as quantity q is given by \(\frac { dC }{ dq } =a-\frac { c }{ q } \) where a is a Constanst. Find C as a function of q.

Solve: 3\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } -5\frac { dy }{ dx } \)+ 2y = 0