16) Solve the differential equation (ædz + ydy + zdz)²z = (2 – 2² – y3)(zdx + ydy + zdz)dz

Q: 1. solve the differential equation: 2t y- y = 0 2. Can these solutions be extended on R?

A: The given differential equation is ,    2t y' - y = 0 Which is a Cauchy - Euler equation of first…

Q: Q4:A/ By using Exact equation solve the first order differential equation 2y² + yexy + (4xy + xexy +…

A: See this solution in below with details.

Q: 12. Solve the second-Order differential equation: d²y - y = e* (use method of variation of…

A:

Q: (b) y" – 9y = e3a

A: To find general solution of differential equation

Q: 4. What is the differential equation of the given functions? • y = Ce-* + Cze-2x + x y = Ce2* +…

A:

Q: Find a suitable form for particular solution of the differential equation y5) + 25y3) = 5 – tešt +…

A:

Q: 1. Solve the linear differential equation of y' – 2xy = = X. swer:

A:

Q: 13 Find solution of non-homogeneous differential equation (D* +1)y = sin (3x)

A: Find complementary function and particular integral

Q: y" – 5y' + 6y = x² + x +1

A:

Q: B: By using Homogenous method solve the first order differential equation (1 + e*%) dx - e²% (-1) dy…

A: We need to solve the differential equation: (1+exy)dx-exy(xy-1)dy=0 first by substituting x=vy we…

Q: a) (2 - 1)y = y² – 1, yı (2) = 1

A:

Q: 1 Solve the differential equation 2 2zy' with the initial condition y (1) = 1.

A: The given differential equation is,1y2-2x=2xy'y3having the initial condition y(1)=1

Q: 5. Solve these differential equations by using the variation of parameters method. 4+36y=csc 3x (b)…

A:

Q: The solution of the differential equation y - 25y = e using the method of reduction of order is

A: y''-25y=e^5x g(x)=e^5x

Q: 3. Find the complete solution of the differential equation (4x + xy2) – (y – x?y)y' = 0 using…

A:

Q: 2yy"=1+y'².

A: We have given differential equation ,  2yy'' = 1 + y'2 Here , substitute y' = u ⇒ y'' = u u'  Thus…

Q: 2. Solve the differential equation: (y² + xy°)dx + (5y² – xy+ y° sin y)dy = 0 by finding an…

A:

Q: 11. Solve the second-order differential equation y" – y' – 2y = 20 cos x using the method of…

A:

Q: 3.(ii) Show that given differential equation is not exact and hence solve it. |(2y – 4xy")dr - (2³ –…

A:

Q: 4. Solve the differential equation 2x(2x – 1)- (x + 1)+y = 0 using the method of Frobenius. dx2…

A: 2x2x-1d2ydx2 +x+1dydx +y=0                       eq.(1) To solve by Frobenius series.

Q: 2x³y' = y(y² + 3x?)

A:

Q: 3. (D² + 4)y = 10 cos 3x. ANS. Y = -2 cos 3

A: We have to find solutions

Q: 5. Solve the differential equation with method of undetermined coefficients. y" + 2y' – 3y = x + cos…

A:

Q: 2. Find the differential equations by eliminating the arbitrary constants of a) y = C₁x + 2² b) y ex…

A:

Q: Find general solutions of the differential equation    2xy+x^2y'=y^2

A: Given

Q: 3x y"+y= e¯x2 - 4x + 2x² + e³x 8-12x - 10x²

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the differential equation…

Q: x(y" + 1) + y² = 0.

A: we have to solve given problems:

Q: Q1/ solve the differential equation - 24 - 2xy with initial condition y(1) = 1.

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 4) Consider the differential equation y" + 8y' + 15y = sin(3t). i) Using the method of undetermined…

A:

Q: 2. Solve the nonhomogeneous differential equation, using the basic rule: y(2) + 6y(1) + 9y =…

A:

Q: Solve the 2nd order differential equation: y"+2y(y')³=0

A:

Q: 4. Solve the differential equation d'y d’y 1 dx dx by the method of variation of parameters extended…

A: A differential equation is an equation that involves derivatives or differential coefficients or…

Q: y" + 25y = 5 tan²(5x) cos(5x)

A: To Determine :-  The second order differential equation : y'' + 25y = 5 tan2  5x cos  5x

Q: Find general solutions of the differential equation      3y^2y'+y^3=e^(-x)

A: Consider the provided differential equation,

Q: Given the differential equation 2 +5 , find the particular solution, y = f(x), 3y with the initial…

A:

Q: 5. Find a general solution of the differential equation: y" + 4y' = 2x – 1

A:

Q: The solution of the differential equation 2r -y = 3 represents a family of O circles straight lines…

A:

Q: Find general solutions of the differential equation  x^3y'=x^2y-y^3

A: the given equation is x3y'=x2y-y3 divide the equation by x3 y'=1xy-1x3y3            ...... (1)…

Q: Solve the Higher Order Differential Equation y'' + 3y + 2y = x^2

A: We have to solve the given higher-order differential equation y''+3y'+y=x2.

Q: Find the complete solution of the differential equation ylv – 2y" + 3y" – 2y' + y = 0

A:

Q: 12. Solve the second-Order differential equation: a²y dx2 -y = e* (use method of variation of…

A:

Q: Find the general solution of the differential equation y" + 5y14y=-62t + 28t². NOTE: Use t as the…

A:

Q: 2+ yеху y' : 2у — хеху

A: The given differential equation is:…

Q: 9) Solve the differential equation y" +3y' +2y= e*. Use the method of Undetermined Coefficients to…

A:

Q: B) Use the method of Undetermined Coefficients to find the general solution of the differential…

A: Introduction: The method of undetermined coefficient is a way to find the particular solution of a…

Q: A/ By using Exact equation solve the first order differential equation 2y² + ye* + (4xy + x² + 2y)y…

A: Topic:- application of differential equations

Q: 3. Solve the differential equation by variation of parameters. y" + 3y + 2y = cos(e*)

A:

Q: - y" – 4y' + 13y = e2*cos3x

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.