Class 12 ISC Maths Chapter Diffrential Equations Exercise 9.1

Access a comprehensive collection of Differential Equations questions, specially designed to help you grasp and apply this important mathematical topic. Our question bank covers various types of differential equations, including first-order, second-order, homogeneous, and non-homogeneous equations, along with real-world applications in physics, engineering, and other fields. These practice questions will help you reinforce your problem-solving skills, deepen your conceptual understanding, and prepare effectively for exams. Whether you're a student or a learner aiming to master Differential Equations, our collection offers the perfect resource for practice and success.

class 12 differential-equations exercise9-1

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Differential-Equations  
Q1
dy / dx
- cosx = 0

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Q2 (
dy / dx
)2 +
dy / dx
- sin2y = 0

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Q3 y’ + y =ex.

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Q4
d2y / dx2
= sin3x + cos3x

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Q5 (x2y — 3x) dy + (x3 - 3y2) dx = 0.

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Q6 √(1-y2) dx + √(1—x2) dy =0.

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Q7
1 / x
.
d2y / dx2
5x
dy / dx
= sin2x

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Q8 (
dy / dx
)4 + 3y
d2y / dx2
= 0

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Q9 (y’)2 + y2 - 1 = 0

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Q10 y” + 5x (y’)2 - 6y = log x.

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Q11 (
d2x / dt2
)4 - 7t (
dx / dt
)3 = log t

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Q12 y(iv) + sin y''' = 0.

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Q13 2x2
d2y / dx2
- 3
dy / dx
+ y = 0.

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Q14 (y”)3 + (y’)2 + sin y’ + 1 = 0.

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Q15 3x
dy / dx
+
5 /
dy / dx
= y3

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Q16 y = x
dy / dx
+ a √(1 + (
dy / dx
)2)

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Q17 y” + (y’)2 + 2y = 0.

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Q18 y” + 2y’ +siny = 0.

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Q19 (y’”)3 +(y”)3 + (y’)4 + y5 = 0.

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Q20 y = px + √(a2p2 + b2) , where p =
dy / dx


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Q21 Write the sum of the order and the degree of the differential equation
(
d2y / dx2
)2 - (
dy / dx
)3 = y3

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Q22 Find the product of the order and degree of the following differential equation :
x (
d2y / dx2
)2 + (
dy / dx
)2 + y2 = 0

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