What is the general solution of (1 + a2) y' = x*y %3D Oy"-3ay + 1 = C O ay - 3ry + 3y% tan-1 æ + 1 = C O"y" - 3ry 3ay 3y tan-1 a + 1 = C O a"y" - 3xys + 3y% tan 1 a – 1 = C

Q: The solution of (e +2ay) daæ + (2 cos 2y+ 2x?y) dy is given by (A) e" + a?y² + cos 2y = c (B) e +…

A: The given equation is; (ex + 2xy2) dx + (2cos2y + 2x2y)

Q: The solution of (e+2xy?) dx + (2 cos 2y + 2x?y) dy is given by (A) e + x?y? + cos 2y = c (B) e +…

A: To find The solution of the given differential equation.

Q: The solution of (e + 2xy?) dx + (2 cos 2y + 2x y) dy is given by (A) e +x'y² + cos 2y = c (B) e"…

A: Given D.E is (ex + 2xy2) dx + (2cos 2y+2x2y) dy = 0     To find the solution of the given D.E .

Q: In(√3) e dx 1+e²x A) tan-¹(3)-tan-¹(e) C) tan-¹(√3) E)-tan-¹(e)

A: Given integral: I=∫1ln3exdx1+e2x   Let, u=ex Then, dudx=ex So, exdx=du Now, the lower limit becomes:…

Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: 1 – s2 S

A: we have to differentiate y  y=cos-1s+s1-s2

Q: (D² - 9)y = 0. (A) y = e*(c,cos2r +c sin2x) B y = c,cosh 3x + c,sinh 3x y = c,cosh – 3x + c,sinh 3x…

A: Solution

Q: 7. Find the rectangular equation if r = 4 cos 0 + 4 sin 0 (a) (c) x² + y² = 4 x² + y² = 4(x + y) (b)…

A:

Q: 1-cos 3x +C 3sin 3x dx 2. 1+ cos 3x

A: We have to prove given integral.

Q: The general solution of (D²+2D+1)(D²+4)y=0 is A y=(C,+C,x)e+C,cos2x + C ,sin2r B) none of the given…

A:

Q: Solve 1- y"- 6y' + 9y 4e Ans. y Ce +c,xex+2x2er

A: Note: Since you have posted multiple independent questions, we will be solving only the first one…

Q: The general solution of y" + 4y' = 12 can %3D be written as (A) y = c1+ c2e¬2= + c3e2 + 3x (B) y=…

A:

Q: y=(b+x²)* +(1+x°)* ( \3x² +x – c )cos²(4x) y'=? %3D %3D

A:

Q: 23 42 R 1 y=2 sinx 2 y = Which equation is represented by the graph? sin 2x 2 1 y-sin 2.r = 2x 1…

A: we need to find the equation of the graph

Q: 13. Differentiate 1 3 y = 2x2 + 6x3 – 2x2 а. 2 6 b. у 3 —t 4 3 x2 3 x4 x2 'x3 y = sin³ [cos(tan(3x –…

A:

Q: Can you explain how all A B C D terms are calculated

A: Solution of the given question is like as

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

A:

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

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Q: In implicit differentation problems it seems we treat x and y differently. For example, when we…

A: Recall: Chain Rule of differentiation :    If F(x)=f(g(x)) then ,   F'(x) = df(g(x))dx =…

Q: Find the general solution (D? + 9)y = 5e* – 162x %3D a. y = c, cos 3x + c2 sin 3x + 18x +e* 2 b. y =…

A:

Q: Solve for the general solution of (D: - 1)y = sinx using variation of parameters y = cje¯* + ¢ze*…

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Q: Solution of 2 y" = 1+y'² is

A: The given differential equation is y''=1+y'2 ......................................... (1)

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A: Given differential equation is 2xsin(3y)dx+3x2cos(3y)dy=0

Q: - فم( (x² – 4)²dx 6. -2 10x4 x3 1 + 15Vx3 – 7) dx 7. 2 3 dx 2x° + x4 8. 1 | (2x + 1)(x – 1) dæ - 9.…

A:

Q: can you find C if x = 1/2 and y = (square root of 2)/2 thank you so so muchh!!

A: