Question

Question 3 (1 mark) Attempt 1 Consider the following second order differential equation: 2 6 d2y +4 dr2 If we let u y and v y' then as an AUTONOMOUS first order system, the second order differential equation is correctly expressed as: dy d.r -y 1+112, with y(1) 9 and y'(1)5 d.r du 6 А dt1, to)1, dtv, u(to)=9, -1+11r2+2u-4v2, v(to)=5. du 6 B dry )9, ar=1+112+y-4(y), v(1)5 du d.r dt du C 1, (1) 0, =v, u(1)=9, -1+11r2+u-4v2, v(1)=5 D (1) 9, d-1+112+u-4v2, v(1)=5 dr du du dt1,to)1, v, u(to)=9, t1+112+v-4u2, v(to)=5 None of these F ш

Answer 1

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SANA Given: - 1+x² with y(1)= 9 & y'll) = 5. d2 7 • Now, uzy & V=Y Solution: - since Also, uzy v= y N = dy - = - du "(1) = 9 (1) = 9 V(!) = y'( 1) = 5 ... 4(1)9) .. V(1) = 5 du div O de = du Adx to x. differentiate both side with respect - Put this value in given differential equation. dv + 4 (0,2-6,= 1+x? 1+x+.- 402 All these values are only available in option -