Q6: Solve the following Higher-Order D.E. d³y d²y dy + 7- 5y = 0 dx 3 %3D - dx3 dx2 To find the values of C, C2, and C3 when y(0) = 1,y(0) = 0, and y"(0) = 0

Q: . Solve: (6x + 1)y² + 3x² + 2y° %3D dr

A:

Q: Evaluate (2x - y) dx + (x + 9y) dy. C: x-axis from (0, 0) to (0, -9) and (0, -9) to (4, -9)

A: Solution :-

Q: Iny y10 (b) S S dy

A: The given integral is:∫ln yy10 dy

Q: (х + у+4)dx+ (x + у—3)dy %3 0

A: The differential equation M(x,y)dx+N(x,y)dy=0 is said to be exact if there exists a function f(x,y)…

Q: (D² +9)y=sec3x

A:

Q: solve the de 2ydx + x(2+x²y)dy=0

A:

Q: Find d²y/dx² implicitly in terms of x and y. x²y - 4x = 6 d²y dx² || (4xy-12) +³ 3 X

A: we need to find out the double derivative of the given expression.

Q: Find an expression for dy/dx. y= (u+5)(u-5) u= x2  + 7

A: Given expression are  y=u+5u-5=u2-52                                Using a+ba-b=a2-b2=u2-25…

Q: + y²(x+ 1)² = C

A:

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

A:

Q: 1. (2л + 5у)dA %3D? D YA (0, 4) у 3 (x + 2)2 X = y - 16 D (-2, 0) (0,-4)

A:

Q: 2y d³y dx3 (y + 3 dx) dy dx² + 2

A:

Q: (d²4)(d-2)y=0

A: To find the roots of  (d2 - 4)(d - 2)y = 0.

Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: IN SA Coefticients 4 Linear in two vanabtes: (x-34+4) dx+2(x-ソ-2)dy

A: In the question it is asked to solve the equation using coefficients linear in two variables:

Q: %3D =D3e %3D 4.

A:

Q: Find the general solution: dy + ycotx = 3eCosx dx y = 3cscx(ecosx) - ccosx b. y = -3cscx(ecosx)+…

A:

Q: -10x Given an equation x3 – y3 = 5, show that y" %3D y5

A: We will show the given statement.

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

A:

Q: C) Solve the equation x = x² + 3y X- dx

A: Given: xdydx=x2+3y

Q: Solve the diff eq (xy² + x- 2y +3)dx + (x³y - 2x – 2y)dy = 0

A:

Q: Ho Find (yor dy d'y ) and (y or -) for the following functions: dx dx L 2. y= x² (x-1)² 5. y=(x²…

A: We need to find the first order and 2nd order derivatives of the given functions.

Q: 2. Determine C when x-y%3D0 show the solutions. (xy + x)dx = (x²y2 + x² + y2 + 1)dy

A:

Q: Find dy dx

A: The given equation is y3+y2-5y-x2=-4. Differentiate both sides with respect to x as follows.

Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 323 2

A: Here to find the value of line integral we consider two path c1 :from the point (0, 0) to (0, -7)…

Q: Determine for which values of m the function (x)=x" is a solution to the given equation. (a) 3,2d…

A: We have to find the value of m.

Q: Find the general solution of the equation: G + 6x) dx + (In x – 2) dy = 0 (x > 0) -

A:

Q: Solve the following equations: 1. (D-D2-2D)y = 0 2. 4Dy-13Dy + 6y = 0 3. D'y - D'y – Dy + y = 0 %3D

A: On solving ist three questions we will get

Q: Find dydx for…

A: the given equation of the curve is: y3+y2-5y-x2+4=0 we have to find the value of dydx

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 4. (x? — у?)dx — 2хydy %3D 0

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.