please solve question 16 differential equations .Q11) The general solution of y" - 4y' +9y = 0, is:a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t)b)y(t) = cet cos(√5 t) + c₂e²sin (√5t)d) y(t) = ce cos(5 t) + c₂esin (5 t)012) The formula of the particular solution yp of y(4) + 4y" = 3 sin(2t) - 5cos2t, is:a) yp= Asin(t) + Bcos(t)c) ypAsin(2t) + Bcos(2t)b) yp = Atsin(t) + Btcos(t)d) yp = Atsin(2t) + Btcos (2t)]Q13) The general solution for y' = 6y²x, is:a) = 3x² + cb)= x² + cc) == 3x² + c d) == x² + cQ14) The solution of y" + y'= 0 by using power series method, is:a) y(x) = ao + a₁(1)c) y(x) = ao + a₁(x-x²x²x²21 31x²x²..)x²b) y(x) = ao + a₂ (1+ 21d)y(x) = ao + a₂(x+:Q15) Given that y₁ (t) = t¹ is solution for 2t²y" + ty' - 3y = 0,t 0, then y₂ (t) is:41 51x5x¹314151)x²=+=a) tb) tzQ16) L-¹ (5-3)²+25)d) tic) tzetsinst5=a)e-3t sin3teatsinstb)est sin3t5C)d)Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t):a)(s+2)²+1625² +18b) (5-2)2+16c)2s²+18(5+2)2+1625+18(S-2)2+1625² +18Q18) Combine the following power series expressions into a single power series.En 1(n+1)(x-2)n-1 + Σon(x - 2)"a) Eno(2n + 1)(x)"b) En-o(2n + 2)(x)"c) Eno(2n + 2)(x - 2)"d)(2n + 1)(x-2)"Q19) The general solution of 2x²y" + 3xy' - 15y = 0, is:a) y(x) = C₁x² + ₂x³b) y(x) = C₁x + ₂x-3c) y(x) = ₂x² + ₂x-3d) y(x) = x² + ₂x³Q20) The form of a particular solution ofy"-4y' - 12y = sin(2t), is:a) yp (t) = A sin(2t)b) y(t) = A cos(t).c) y(t) = A cos (2t) + B sin(2t)d) y(t) = A cos(t) + B sin(t)Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x):a) f(x), g(x) and h(x) are linearly dependentc) W (f(x), g(x), h(x)) = 0b) f(x), g(x) and h(x) are linearly independed) W (f(x), g(x), h(x)) = 9=is:(3s+2)(S-2)S'Q22) The inverse Laplace transform of H(s)b) f(t)= e+e-a) f(t) ==e¹+¹e²t-3 -28-2,c) f(t) = ¹ + 1 ee-2td)f (t) ==³e²¹ +²e²tQ23) The kernel of the Laplace transform of f(t), t 0, is:b) e-tc) e-std) e-sa) eQ24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is:a) e-3xb) exd) e 3xb) -2sinhntc)-2cosntd) -2sinntQ25) L-1-2sS²+T²a) -2coshnt=·+...)

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please solve question 16 differential equations .Q11) The general solution of y&#34; - 4y' +9y = 0, is:a) y(t) = c₂e2t cos(5 t) + c₂e2t sin (5 t)c)y(t) = c₂e2t cos(√5 t) + c₂e²t sin (√5 t)b)y(t) = cet cos(√5 t) + c₂e²sin (√5t)d) y(t) = ce cos(5 t) + c₂esin (5 t)012) The formula of the particular solution yp of y(4) + 4y&#34; = 3 sin(2t) - 5cos2t, is:a) yp= Asin(t) + Bcos(t)c) ypAsin(2t) + Bcos(2t)b) yp = Atsin(t) + Btcos(t)d) yp = Atsin(2t) + Btcos (2t)]Q13) The general solution for y' = 6y²x, is:a) = 3x² + cb)= x² + cc) == 3x² + c d) == x² + cQ14) The solution of y&#34; + y'= 0 by using power series method, is:a) y(x) = ao + a₁(1)c) y(x) = ao + a₁(x-x²x²x²21 31x²x²..)x²b) y(x) = ao + a₂ (1+ 21d)y(x) = ao + a₂(x+:Q15) Given that y₁ (t) = t¹ is solution for 2t²y&#34; + ty' - 3y = 0,t> 0, then y₂ (t) is:41 51x5x¹314151)x²=+=a) tb) tzQ16) L-¹ (5-3)²+25)d) tic) tzetsinst5=a)e-3t sin3teatsinstb)est sin3t5C)d)Q17) Evaluate L (2 e-2t sin4t - 0.5 cos3t):a)(s+2)²+1625² +18b) (5-2)2+16c)2s²+18(5+2)2+1625+18(S-2)2+1625² +18Q18) Combine the following power series expressions into a single power series.En 1(n+1)(x-2)n-1 + Σon(x - 2)&#34;a) Eno(2n + 1)(x)&#34;b) En-o(2n + 2)(x)&#34;c) Eno(2n + 2)(x - 2)&#34;d)(2n + 1)(x-2)&#34;Q19) The general solution of 2x²y&#34; + 3xy' - 15y = 0, is:a) y(x) = C₁x² + ₂x³b) y(x) = C₁x + ₂x-3c) y(x) = ₂x² + ₂x-3d) y(x) = x² + ₂x³Q20) The form of a particular solution ofy&#34;-4y' - 12y = sin(2t), is:a) yp (t) = A sin(2t)b) y(t) = A cos(t).c) y(t) = A cos (2t) + B sin(2t)d) y(t) = A cos(t) + B sin(t)Q21) One of the following is correct for functions the f(x) = 1, g(x) = x³ and h(x) = ln(x):a) f(x), g(x) and h(x) are linearly dependentc) W (f(x), g(x), h(x)) = 0b) f(x), g(x) and h(x) are linearly independed) W (f(x), g(x), h(x)) = 9=is:(3s+2)(S-2)S'Q22) The inverse Laplace transform of H(s)b) f(t)= e+e-a) f(t) ==e¹+¹e²t-3 -28-2,c) f(t) = ¹ + 1 ee-2td)f (t) ==³e²¹ +²e²tQ23) The kernel of the Laplace transform of f(t), t > 0, is:b) e-tc) e-std) e-sa) eQ24) The Integrating factor which make (3x2y + 2xy + y³) dx + (x² + y²)dy = 0 exact, is:a) e-3xb) exd) e 3xb) -2sinhntc)-2cosntd) -2sinntQ25) L-1-2sS²+T²a) -2coshnt=·+...)

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t b) tz 16) L-¹ (5-3)²+25) = c) tz estsinst a) 5 d) t est sin3t 5 b) c) e-at sin3t 5 eatsinst d)