(3sin y– 5x)dx+2x² cot ydy = 0 3.

Q: Obtain the general solution por the di fferential equation %3D .(yd -x² )dy= 2xy dx %3D

A: Given; 1) y'=(x-y)/y. 2) (y2-x2)dy=2xydx.

Q: Find a solution to the euler equation, from : rx2 (2? – y/²)dx

A:

Q: Use Picard's method to solve dx - Find y3(1)? -xy, y (0) = 1

A: Solution :-

Q: 7 1. 2ydx+x²dy = - dx; y = - when x =1 In 2 2

A: Given:- 2y dx +x2 dy =-dx  To find:- Solution of Differential equation at y = 7/2 when x =1/ln(2)

Q: dy dx dx tan x+1. Solve by using the method of variation of parameter

A: To solve by using the method of variation of parameter d3ydx3+dydx=tan2x+1

Q: dx Integrate by trigonometric substitution: .2 4x² -9 2

A: Given integral :

Q: Q3 Integrate using trigonometric substitution: dx I To +x² /9 +

A: Let (x/3) = tant Differentiate on both side  dx/3 = sec2t.dt dx = 3.sec2t.dt

Q: 1. y = 5sin 3x*

A:

Q: Determine the type of equation and find a general solution. dy/dx = (sinx + cosx)/ (y^2-1) show…

A:

Q: Q3) find the soluation of differention equation 2) y' sin 2x = y cos 2x

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Q: dy - x X, y(0) = -4 dx Need Help? Watch It

A: using variable separable and then integrate both side...

Q: rcosA 2. r sin 0 dz dr de

A:

Q: Siven the equation y 4 sin(6x – 18) +5 %3D -

A: We have a standard form, a sin(bx+c) +or- d Comparing it with the given equation we have, a= 4 b= 6…

Q: -2 Ssin®(3x)cos(3x) 5 dx

A: Given, ∫sin53xcos3x-25dx We have to find the integration.

Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

A:

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: Use the Errors in the Trapezoidal Rule and Simpson's Rule cos(4nx) dx

A:

Q: Solve the equation using suggested substitution: (3siny-5x)dx + 2x2cotydy = 0; let z = siny

A:

Q: Use this equation to find dy/dx. 4y cos(x) = x² + y2

A: We will differentiate  equation with respect to X.

Q: Use variation of parameters to find the particular solution to y"+y' – 20y = - 3400 sin(3t) Y(t) = |…

A:

Q: for the equation dx ecosh-(x) = In(x) sinh-(y) Find %3D

A: Using differentiation of   product rule and implicit differentiation,

Q: y" + y = sin t

A: Explanation of the solution is given below...

Q: Solve (1 + y) dx = (tanly-x) dy

A:

Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i и

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Q: y=x√3-2x³

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Q: Find the solution of the DE using reduction Order (D2 + 4)y = sinx

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Q: Solve dy/dx + 2y = 4, y(0) = 3 by one of the usual methods. Solve same the problem by Picard’s…

A: Integrating factor method for solving a differtial equation  Consider the differtial equation…

Q: Test the equation for exactness and if separable: (2xy + 2x) dx = y dy

A:

Q: d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

A: d2ydx2+4y=4tan2x

Q: d?x + 4x = sin2t Q5: Solve: %3D dt2 Using variation of parameters method?

A: Answer

Q: -x2 + 5 2. y = cos 2x³

A: Given: y=-x2+5cos2x3

Q: Solve dy dy + y = 2sin(3x) - dx? dx using the method of undetermined coefficient.

A: We solve the given differential equation by method of undetermined coefficients.

Q: 7. (1+ 2e"/»)dx + 2e*%» (1-) dy = 0

A:

Q: Find d2y/dx2 implicitly in terms of x and y 7xy + sin x = 2

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Q: Find the solution to the Bernoulli Equation. (3siny-5x) dx + 2x² cotydy=0

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Q: - y = V1 – sinx

A: Given,y=1-sinx3y=1-sin(x)13Differentiate w.r.t. x using chain…

Q: Solve = 1 +y, y(0) = 0 by Picard's method. %3D dx

A:

Q: For which value of a the equation dz dy dx =2 -1 does hold?

A: The constant rule of integration and the power rule of integration are given by and, respectively,…

Q: SOLVE USING THE METHOD OF VARIATION OF PARAMETERS d³y , dy 1 V1- cos²(x) dx3 dx .2 II

A: This given equation is third order non homogeneous ordinary Differential  Equation to solve this we…

Q: find the dy/dx of sin(sqrt(y))+2xy=-y^7

A: Given: siny+2xy=-y7 To Find: dydx=?

Q: Give what is asked. Find dy/dx. Show your solution.

A: Simplify the equation and differentiate it.

Q: Solve using the variation of parameters d'y/dx + dy/dx 1/Sqr(1-cos²x)| %3D

A:

Q: Use this equation to find dy/dx. 8y cos(x) = x2 + y2 dy dx II

A: Given  8y cos(x)=x2+y2We find dydx

Q: For which value of a the equation dz dy dx =2 does hold?

A: as per guidelines we only solve one question at a time if you want to know the answer of all please…

Q: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: Use Variation of Parameters to solve the DE y" – 4y %3D

A: Given differential equation y''−4y=e2xx Write the auxiliary equation m2−4=0 ⇒m2=4⇒m=±2 Hence,…

Q: Find dy/dx at the given point without first solving for y. x2 — бу — 37 %3D0 at (1, -6) | dy dx

A: This question is based on derivative.

Q: 10. y = cos In 7x6

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.