Test of Differential equation

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.