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- Find y as a function of t if 7y" + 28y = 0, y(0) = 4, y'(0) = 3. y(t) Note: This particular weBWork problem can't handle complex numbers, so write your answer in terms of sines and cosines, rather than using e to a complex power.4. Verify that the functions 1, r, cos r and sinr form a funda- mental set of solutions of y(4) + y" = 0 on (-0o, 00).Find all the singular points for the differental equation and classify each as regular or irregular. Dont slove the equation. (x2+x-6)y'' + (x +3)y' + (x-2)y = 0
- 3. Let r,, r, and r, be the roots of x' +3x² -5x-4=0, construct the equation whose roots are: 7 (r, + r3 ), rz (r, +x) and r, (r +r, ). F12 PrtScr Insert Delete F8 F9 F10 F11Let f(z) = iz³ + cos(z²) z² +1 i. Find ƒ'(z). ii. Evaluate f'(−2i) and simplify. iii. State the points in the complex plane at which the derivative is undefined. iv. State, giving reasons, whether or not f(z) is entire.Compute the derivatives of the given functions. b) [12 cos¯¹2x] d dx c) d) e) f) d. du d dz d dy d dq [4 sec ¹3u] [10 tan-¹2z -1 [6 csc ¹ 4y] [9 cot-¹39] = = = = = G 4. 9- FI
- 25. Find pairs of solutions of Laplace's equation, = 0, based on these complex functions: (a) ze2: (b) z*: (c) z sin z: (d) e cosz. ...****** ********..1 of 17 > Find the equation of the tangent plane to the graph of f(x, y) = In (14x² – 11y²) at the point (1, 1). (Use symbolic notation and fractions where needed. Enter your answer using x-, y-, z-coordinates.) the equation:Prove that a parametric function given by I= 2t + 31 y = t² + 2t* satisfies the equation v- (2)' • •(2)' dr dr
- in pictureWhich of the following pair of functions is linearly independent? (а) еЗx, е(х-3) (b) 4, sin?x + cos?x (c) 2sin2x, sinxcosx (d) sinhx, (e* – e*)the exponents at the singular point x=2 (the roots of the indicial equation) for (x – 2)²(x + 1)y" + 3(x² + x - 6)y' + (4x + 1)y = 0: are : Select one: a.r = -1,3 b. NOTA c. r=-1 ,-3 d.r = 2,3 e. r= 1 ,-3