Write the degree of the differential equation: \(5x{ \left( \frac { dy }{ dx } \right) }^{ 2 }-\frac { { d }^{ 2 }y }{ { dx }^{ 2 } } =0.\)

Write the sum of the order and degree of the differential equation \(1+\left( \frac { dy }{ dx } \right) ^{ 4 }=7\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 3 }\)

Write the degree of the differential equation \({ x }^{ 3 }\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) ^{ 2 }+x\left( \frac { dy }{ dx } \right) ^{ 4 }=0\)

Find the differential equation representing the family of curves \(V=\frac { A }{ r } +B\) , where A and B arbitrary constants.

Find the integrating factor of the differential equation \(\left( \frac { { e }^{ -2\sqrt { x } } }{ \sqrt { x } } -\frac { y }{ \sqrt { x } } \right) \frac { dx }{ dy } =1\) .

Find the sum of the order and degree of the following differential equations :
\(\frac { { d }^{ 2 }y }{ dx^{ 2 } } +\sqrt [ 3 ]{ \frac { dy }{ dx } } +\left( 1+x \right) =0\)

Find the general solution of differential equation \(\log { \left( \frac { dy }{ dx } \right) } =x+1\)

Find the general solution of the differential equation: \((x-y){dy\over dx}={x+2y}\)

Find the equation of the curve passing through the point (1, 1) whose differential equation is x dy = (2x² + 1) dx, (x\(\neq \)0).

Show that the family of curves for which the slope of the tangent at any point (x, y) on it is \(\frac { { x }^{ 2 }+{ y }^{ 2 } }{ 2xy } ,\) is given by  \({ x }^{ 2 }-{ y }^{ 2 }=cx.\)

Form the differential equation of the family of ellipses having foci on x-axis and centre at origin

Which of the following differential equations has y=x as one of its particular solution?
(A) \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -{ x }^{ 2 }\frac { dy }{ dx } +xy=x\)
(B) \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } +{ x }\frac { dy }{ dx } +xy'=x\)
(C) \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -{ x }^{ 2 }\frac { dy }{ dx } +xy=0\)
(D) \(\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -{ x }\frac { dy }{ dx } +xy=0.\)

Solve the differential equation:\(sec x\frac { dy }{ dx } -y=sin\quad x.\)

Solve \(\left( x^{ 2 }-1 \right) +2xy=\frac { 2 }{ { x }^{ 2 }-1 } .\)

Find the particular solution of the differential equation:
\(\left( 1+{ x }^{ 2 } \right) \frac { dy }{ dx } ={ e }^{ m{ tan }^{ { -1 }_{ x } } }-y,\) given that \(y=1\) when \(x=0\)

Solve the differential equation : \(\frac {dy}{dx} \) + y = cos x - sin x

Show that Px² + Qy² = 1 is a solution of differential equation x[yy₂ + y₁²] = yy₁.

An engineer finds out that there dependence. F(x) on hours worked x, as \(F\left( x \right) P+\frac { Q }{ { x }^{ 2 } } \), where P and Q are the constants or different employess of his company. Express a differential equation between F(x) and x. What do you observe with the charge in efficiency of employees with increase their working hours ?

Find the particular solution of the differential equation \(\frac { dy }{ dx } =\frac { xy }{ { x }^{ 2 }+{ y }^{ 2 } } \) given that y = 1, when x = 0.