Chapter 9: Differential Equations

NCERT Solutions for CBSE Class 10 Mathematics — 16 solved questions with detailed explanations.

Questions

Topics

Solved Questions

Q1. The degree of dy/dx + (dy/dx)³ = x² is:

1
2
3
Not defined

Difficulty: Easy-Medium · Topic: Degree and Order

Solution

The highest power of dy/dx is 3. Degree = 3. (Order = 1).

Q2. The solution of dy/dx = y/x is:

y = Cx
y = C/x
y = Cx²
y = Ce^x

Difficulty: Easy-Medium · Topic: Separation of Variables

Solution

dy/y = dx/x. ln|y| = ln|x| + C₁. y = Cx (linear relationship).

Q3. The integrating factor of dy/dx + y/x = x is:

Difficulty: Easy-Medium · Topic: Integrating Factor

Solution

IF = e^(∫ 1/x dx) = e^(ln x) = x.

Q4. Order of d²y/dx² + 3dy/dx + y = 0 is:

Difficulty: Easy-Medium · Topic: Differential Equations

Solution

Q5. Degree of (dy/dx)² + dy/dx = x is:

1
2
3
not defined

Difficulty: Easy-Medium · Topic: Differential Equations

Solution

Q6. A homogeneous DE can be solved by substitution:

y = vx
y = x²
y = e^x
y = x+v

Difficulty: Easy-Medium · Topic: Differential Equations

Solution

y = vx.

Q7. Order of dy/dx = x+y:

Difficulty: Easy-Medium · Topic: DE Order

Solution

Highest derivative order = 1.

Q8. Degree of dy/dx = x+y:

Difficulty: Easy-Medium · Topic: DE Degree

Solution

Highest power of highest derivative = 1.

Q9. Order of d²y/dx² + y = 0:

Difficulty: Easy-Medium · Topic: DE Order

Solution

Highest derivative order = 2.

Q10. Degree of d²y/dx² + y = 0:

Difficulty: Easy-Medium · Topic: DE Degree

Solution

Highest power of highest derivative = 1.

Q11. Order of (dy/dx)³ + dy/dx = x:

Difficulty: Easy-Medium · Topic: DE Order

Solution

Highest derivative order = 1.

Q12. Degree of (dy/dx)³ + dy/dx = x:

Difficulty: Easy-Medium · Topic: DE Degree

Solution

Highest power of highest derivative = 3.

Q13. Order of d³y/dx³ + x(dy/dx) = 0:

Difficulty: Easy-Medium · Topic: DE Order

Solution

Highest derivative order = 3.

Q14. Degree of d³y/dx³ + x(dy/dx) = 0:

Difficulty: Easy-Medium · Topic: DE Degree

Solution

Highest power of highest derivative = 1.

Q15. Order of d²y/dx² + (dy/dx)² + y = 0:

Difficulty: Easy-Medium · Topic: DE Order

Solution

Highest derivative order = 2.

Q16. Degree of d²y/dx² + (dy/dx)² + y = 0:

Difficulty: Easy-Medium · Topic: DE Degree

Solution

Highest power of highest derivative = 1.

Other Chapters in Mathematics

Ch 1: Relations & Functions Ch 2: Inverse Trig Functions Ch 3: Matrices Ch 4: Determinants Ch 5: Continuity & Differentiability Ch 6: Applications of Derivatives Ch 7: Integrals Ch 8: Applications of Integrals Ch 10: Vector Algebra Ch 11: Three Dimensional Geometry Ch 12: Linear Programming Ch 13: Probability

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