Which of the following equations is/are exact? (3x²y – x²) dx + e#*, dy = 0 3x?y? dx + (2x°y+ 4y³) dy = 0 O (y + 2xy³) dæ + (1+ 3x²y? + ) dy = 0 O (xy+ 1) dx + (xy – 1) dy = 0 -

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

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Q: Which of the following is a linear equation? O 2ay'dy = (2æ² – y^) dæ I| O sin æ cos? æ dy = (1 – y…

A: We need to find out the linear differential equation, from the given ODEs. This can be done as…

Q: which of the following is equation is an exact DE? a. (x^2 + 1)dx + xydy = 0 b. xdy + (3x- 2у) dx…

A: which of the following equation is exact DE? (i) x2+1dx+xydy=0 (ii) xdy+3x-2ydx=0 (iii) 2xy…

Q: Which of the following is the particular solution to the DE y(9x – 2y)dx – x(6x – y)dy = 0; y(1) =…

A: Given differential equation is y9x-2ydx-x6x-ydy=0 and y1=1 Given differential can be written as:…

Q: Which of the following is an exact DE? A. (x² + 1)dx - xydy = 0 B. xdy + (3x - 2y)dx = 0 C. 2xydx…

A: Solution:

Q: Which of the following equations is a variable separable DE? O a. 2y dx = (x² + 1) dy O b. y? dx +…

A: Using differential equations,

Q: Transform the equation (a'y – 3y) y' + æy variable separable form o into a %3D | f (x) dx + g (y) dy…

A: We know,  A variable separable differential equation is the method to solve differential equation in…

Q: Which of the following equations is NOT an exact equation? A (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: Find the solution of ordinary differentral equation X+2xy'-2y=L4xlox -5cos(Inx)

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Q: Which of the following equations is an exact DE? a. 2xy dx + (2 + x²) dy = 0 O b. x²y dy - y dx = 0…

A: To find Which of the given equations is an exact.

Q: Which of the following equations is NOT an exact equation? A ( xy - cos y) d x + ( x² + 1) dy = 0 (B…

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Q: Which of the following gives the length of the graph of x = y3 from y = - 2 to y=2? 1+y° dy |1+9y*…

A: sol given   x= y       y = -2 to y = 2   arc length = ∫y =ay= b 1+ (g1 (y)2 dy

Q: 3. Solve the DE dy = x + 2x %3D a. dx 3 dy b. dx %3D dy C. -= 4 cos 6x %3D dx

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Q: Which of the following is true if 2x y = 5 + "e* dt a. and y(1) = 5 e dx O b. dy 2eAx and y(0) = 5…

A: Explanation of the answer is as follows

Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

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Q: z=9x + 4y + 1 dy = (9x+4y+ 1) 2 reduces to dx Using the substitution the DE -- dz=9dx+ 4dy

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Q: Which of the following equations is an exact DE? A (x²+1) dx - xy dy = 0 (B) x dy + (3x-2y) dx = 0…

A: Exact and non exact differential equations

Q: 2-(3%3-6%y)dx-(322+2y)dyso 3-(2%y%+siny)dx+(43y²+žcosy)dyso,

A: we given some differential equation . As per our guidelines I can only solve first question or first…

Q: The equation (tan?x+3y²)sec?xdx+(3tan?x+y²)dy= 0 can be solved by A Bernoulli's Equation B…

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Q: dy Let y=e* sin 3x. Show that 3e-2* cos 3x - 2y. dx -2x d'y = -13y-4- dr Hence show that dx

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Q: The point of intersection when the coefficients of dx & dy are equated to zero of the given DE:…

A: Here I am attaching image so that you understand each and every step.

Q: 3. Given: y = f (u) and u = g(x), find dy/dx: %3D 2u d) у 3 u = 10x² + x + 1 (u²+1)' e) y = u+ cos'…

A: We have to solve given problem:

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy² 2x3 + x²y +y³ b.…

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Q: xy*dx + x?dy, where C is the le with vertices (0,0), (4,0), (4,5), and

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Q: hat is the answer for this DE? 1.) (2x - y) dx + (4x + y - 6) dy = 0

A: We need to find the solution of the DE(2x - y) dx + (4x + y - 6) dy = 0

Q: Which of the following equations is NOT an exact equation? A cos y dx - (x sin y - y?) dy = 0 B)…

A: Given the differential equations

Q: Which of the following equations is(are) true? 1 2x du I. -dx x² + 1 S 5.² o √u √2 1 2x II. -dx 10…

A: Given: I=∫012xx2+1dx   ...1

Q: 10. The following equations are exact except (2xy – y)dx + (x² – x)dy = 0 b. 2xydx + (y? +x² )dy = 0…

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Q: Which of the following equations is an EXACT Equation? (A) (2ху — у)dх + (x2+ х)dy %3D о dy B 2xy +…

A: Topic = Differential equation Correct option = B   A differential equation of type P(x,y) dx +Q(x,y)…

Q: Solve the following equations: a) y√(1-x²)dy + x√√(1- y²)dx=0 dy x(2 ln x+2) b) = dx sin y+y cos y y…

A: To integrate.

Q: III. Find the particular solution of each of the following. dx 1. dy 2x - 7y*; when y=1,x=-1

A: Find the particular solution of each of the following. dxdy+2xy=7y4; when y=1, x=-1

Q: Which of the following equations is/are exact? □ 3x²y² dx + (2x³y + 4y³) dy = 0 (3x²y-x²) dx + e³ dy…

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Q: Show if the following statement is true or false. If it is true, write TRUE. If it is false, write…

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Q: Which of the following equations is NOT an exact equation? dy=0 B (xy - cos x)dx + (x² – 1)dy=0 (2x…

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Q: Which of the following equation is a variable separable DE? a. (x + x^2y) dy = (2x + xy^2) dx b. (x…

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Q: Is this 2-form exact? w = x dx A dy

A: Given that ω=xdx∧dy To check this  2-form is  exact or not.

Q: Find regular singular points of the defferential equation. d²y dy 2x? +(x² - 4) y = 0 +3x dx? dx

A: Given differential equation is 2x2d2ydx2 + 3xdydx + (x2-4)y = 0

Q: 7. Find dyldx given the following implicit equation: x²y²-y= x c. dy dy 1-2xy2 dx 2x²y-1 a. 1 %3D dx…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: 3. Which of the following gives if y=sin" (2x)? dx 2 (A) V1-4x 1 (B) V1- 4x 2 (C) V1-4x 1 (D) V1-4x…

A: To find the dy/dx

Q: Find the general solution of the following: d'y dy -2 +2y=- dx csc(x) CSC dx2 1. MVP: et…

A: As per our guidelines we are supposed to solve only one question. So please upload the other…

Q: *?Which of the following equations Is an exact differentlal equation (x² + 1) dx – xydy = 0 2xydx +…

A: We have to choose correct options.

Q: Which of the following equations is NOT an exact equation? (2x sin y + y)dx + (x² cos y + x)dy = 0…

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Q: 7. Find fSp(x - y)*dx dy, where D is Figure 17.2.13. y A シ=V ソ=2-

A: Answer is 64/35

Q: a) Find dy/dx and d²y/dx² at the given point without eliminating the parameter x= 0+ cos 0, y=1+ sin…

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Q: Find the general soultion of the follwoing equations dy cos x + y = cos²x, dx *+ y = xy/3.

A: Differential equation

Q: The roots of the characteristic equation of (D² + D+ Dy = 0 %3D are A1 = -1+ 3i and A2 = -1 – 3i .

A: See the solution step by step.

Q: Is the equation separable, linear, bernoulli, or homogenous? dy а. dx x4 + 4xy2 2.13 + x²y +y³ b.…

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Q: d²y then dx² cos x 2 dy Show that if y -+y = 0 x dx %3D

A: Given: y=cosxx To show: d2ydx2+2xdydx+y=0 Differentiate y with respect to x using the quotient rule…

Q: Which of the following is an exact DE? A none of the given choices B) csc (x²+1) y' – xcosy dy=0…

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Q: Which of the following equations is a homogenous DE? O (xy? + x)dx + (x²y- y)dy=D0 O (x- y)dx+ (3x+…

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