Class 12 CBSE Applied Maths Differential Equations Exercise 8.5

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.

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Q1. Which of the following equations are linear differential equations of first order in y?

(i) x² dy/dx - 2xy = x³ + 2x² − 5
(ii) x log x dy + (3y – 5 log x) dx = 0.

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Q2. Which of the following equations are linear differential equations of first order in x?

(i) dx/dy - 2x/y =3y³-5y+1
(ii) dx/dy - 2x/y =3y³-5y+1

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Q3. Write an integrating factor of each of the following linear differential equation :

(i)y dx − (x + 2y²) dy = 0, y > 0
(ii) y e^y dx = (y³ + 2x e^y) dy, y ≠ 0
(iii) dx +xdy=(e^-ylog y)dy,y>0

(iv) (1-y²)dx/dy +yx=ay,|y|< 1

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Q10. Solve the differential equation (1+x²)dy/dx+2xy-4x²=0 subject to the intial condition y(0)=0

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Class 12 CBSE Applied Maths Differential Equations Exercise 8.5

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Q1. Which of the following equations are linear differential equations of first order in y? (i) x² dy/dx - 2xy = x³ + 2x² − 5 (ii) x log x dy + (3y – 5 log x) dx = 0.

Q2. Which of the following equations are linear differential equations of first order in x? (i) dx/dy - 2x/y =3y3-5y+1 (ii) dx/dy - 2x/y =3y3-5y+1

Q3. Write an integrating factor of each of the following linear differential equation : (i)y dx − (x + 2y²) dy = 0, y > 0 (ii) y ey dx = (y3 + 2x ey) dy, y ≠ 0 (iii) dx +xdy=(e-ylog y)dy,y>0 (iv) (1-y2)dx/dy +yx=ay,|y|< 1

Q4. (i) dy/dx+y/x=x2 (ii)x dy/dx + 2y=x2

Q5. (i) dy/dx + 2y=6ex (ii) dy/dx + 3y=e-2x

Q6. (i) (1+x2)dy/dx=4x2-2xy (ii) dy/dx+y/x=e-x

Q7. (i) xdy/dx +y=x logx (ii) xdy/dx + 2y=x2 logx

Q8. (i) y dx +(x-y2)dy=0,y>0 (ii) (x+2y3)dy=ydx,y>0

Q9. (i) dx+ xdy=e-ylog y dy,y>0 (ii) (x+2y3)dy=ydx,y>0

Q10. Solve the differential equation (1+x2)dy/dx+2xy-4x2=0 subject to the intial condition y(0)=0

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Q1. Which of the following equations are linear differential equations of first order in y?

(i) x² dy/dx - 2xy = x³ + 2x² − 5
(ii) x log x dy + (3y – 5 log x) dx = 0.

Q2. Which of the following equations are linear differential equations of first order in x?

(i) dx/dy - 2x/y =3y³-5y+1
(ii) dx/dy - 2x/y =3y³-5y+1

Q3. Write an integrating factor of each of the following linear differential equation :

(i)y dx − (x + 2y²) dy = 0, y > 0
(ii) y e^y dx = (y³ + 2x e^y) dy, y ≠ 0
(iii) dx +xdy=(e^-ylog y)dy,y>0

(iv) (1-y²)dx/dy +yx=ay,|y|< 1

Q4. (i) dy/dx+y/x=x²
(ii)x dy/dx + 2y=x²

Q5. (i) dy/dx + 2y=6e^x
(ii) dy/dx + 3y=e^-2x

Q6. (i) (1+x²)dy/dx=4x²-2xy
(ii) dy/dx+y/x=e^-x

Q7. (i) xdy/dx +y=x logx
(ii) xdy/dx + 2y=x² logx

Q8. (i) y dx +(x-y²)dy=0,y>0
(ii) (x+2y³)dy=ydx,y>0

Q9. (i) dx+ xdy=e^-ylog y dy,y>0
(ii) (x+2y³)dy=ydx,y>0

Q10. Solve the differential equation (1+x²)dy/dx+2xy-4x²=0 subject to the intial condition y(0)=0