This document lists 7 problems involving differential equations: 1) Find the order and degree of a given differential equation. 2) Find the differential equation of a family of lines passing through the origin. 3) Form the differential equation of a family of circles with centers on the y-axis and radius of 3 units. 4) Find the general solution of a given differential equation. 5) Solve a given differential equation involving radicals. 6) Show that a given differential equation is homogeneous and find its particular solution. 7) Solve a given differential equation involving radicals.

1. 1. Findthe orderand degree of y = x
𝑑𝑦
𝑑𝑥
+ a √1 + (
𝑑𝑦
𝑑𝑥
)
2
2. Findthe differential equationof familyof linespassingthroughorigin.
3. Form the differential equation of the family of circles having centre on y – axis and radius 3 units.
4. Find the general solution of the differential equation
𝑑𝑦
𝑑𝑥
- y = cos x.
5. Solve the following differential equation : √1 + 𝑥2 + 𝑦2 + 𝑥2 𝑦2 + 𝑥𝑦
𝑑𝑦
𝑑𝑥
= 0 .
6. Show that the differential equation : 2y ex/y
dx + (y – 2x ex/y
) dy = 0 is homogenous and find its
particular solution, given x = 0 when y = 1.
7. Solve the Differential equation: x2
y dx – (x3
+ y3
) dy = 0.
1. Findthe orderand degree of y = x
𝑑𝑦
𝑑𝑥
+ a √1 + (
𝑑𝑦
𝑑𝑥
)
2
2. Findthe differential equationof familyof linespassingthroughorigin.
3. Form the differential equation of the family of circles having centre on y – axis and radius 3 units.
4. Find the general solution of the differential equation
𝑑𝑦
𝑑𝑥
- y = cos x.
5. Solve the following differential equation : √1 + 𝑥2 + 𝑦2 + 𝑥2 𝑦2 + 𝑥𝑦
𝑑𝑦
𝑑𝑥
= 0 .
6. Show that the differential equation : 2y ex/y
dx + (y – 2x ex/y
) dy = 0 is homogenous and find its
particular solution, given x = 0 when y = 1.
7. Solve the Differential equation: x2
y dx – (x3
+ y3
) dy = 0.
1. Findthe orderand degree of y = x
𝑑𝑦
𝑑𝑥
+ a √1 + (
𝑑𝑦
𝑑𝑥
)
2
2. Findthe differential equationof familyof linespassingthroughorigin.
3. Form the differential equation of the family of circles having centre on y – axis and radius 3 units.
4. Find the general solution of the differential equation
𝑑𝑦
𝑑𝑥
- y = cos x.
5. Solve the following differential equation : √1 + 𝑥2 + 𝑦2 + 𝑥2 𝑦2 + 𝑥𝑦
𝑑𝑦
𝑑𝑥
= 0 .
6. Show that the differential equation : 2y ex/y
dx + (y – 2x ex/y
) dy = 0 is homogenous and find its
particular solution, given x = 0 when y = 1.
7. Solve the Differential equation: x2
y dx – (x3
+ y3
) dy = 0.
1. Findthe orderand degree of y = x
𝑑𝑦
𝑑𝑥
+ a √1 + (
𝑑𝑦
𝑑𝑥
)
2
2. Findthe differential equationof familyof linespassingthroughorigin.
3. Form the differential equation of the family of circles having centre on y – axis and radius 3 units.
4. Find the general solution of the differential equation
𝑑𝑦
𝑑𝑥
- y = cos x.
5. Solve the following differential equation : √1 + 𝑥2 + 𝑦2 + 𝑥2 𝑦2 + 𝑥𝑦
𝑑𝑦
𝑑𝑥
= 0 .
6. Show that the differential equation : 2y ex/y
dx + (y – 2x ex/y
) dy = 0 is homogenous and find its
particular solution, given x = 0 when y = 1.
7. Solve the Differential equation: x2
y dx – (x3
+ y3
) dy = 0.