document.write( "Question 1152830: If dy/dx is 6x^2+4x-5, and y=10 when x=2, find the value of y when x=3. please with full working \n" ); document.write( "
Algebra.Com's Answer #774926 by ikleyn(52776)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            It is very standard Calculus problem, typical for beginner Calculus students,\r
\n" ); document.write( "\n" ); document.write( "            and the solution by @MathLover1 is   A B S O L U T E L Y   W R O N G.\r
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\n" ); document.write( "\n" ); document.write( "            Below find the correct solution,  instead.\r
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document.write( "Consider ANTIderivative, which is the general solution to the given differential equation\r\n" );
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document.write( "    y = 2x^3 + 2x^2 - 5x + C,    (1)\r\n" );
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document.write( "where C is an arbitrary constant.\r\n" );
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document.write( "We define the value of this constant from the given condition y= 10 at x= 2.\r\n" );
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document.write( "Substitute x= 2 into (1) to get\r\n" );
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document.write( "    10 = 2^2^3 + 2*2^2 - 5x + c,\r\n" );
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document.write( "    10 = 2*8 + 2*4 - 5*2 + C = 16 + 8 - 10 + C = C + 14,\r\n" );
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document.write( "which implies\r\n" );
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document.write( "    C = 10 - 14 = -4.\r\n" );
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document.write( "So, the specific solution to the given differential equation under the given condition at the point x= 2 is\r\n" );
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document.write( "    y = 2x^3 + 2x^2 - 5x - 4.    (2)\r\n" );
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document.write( "Now the value of y at x= 3 is\r\n" );
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document.write( "    y = 2*3^3 + 2*3^2 - 5*3 - 4 = 53.      ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Having this text before your eyes,  printed or in the screen of your computer,\r
\n" ); document.write( "\n" ); document.write( "you may boldly go to a  Calculus class and to give a  PRESENTATION  (a lecture)\r
\n" ); document.write( "\n" ); document.write( "to students,  using my post as a  mantra,  even if you do not understand the subject,  at all.\r
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\n" ); document.write( "\n" ); document.write( "You may use this post for many other similar problems,  with the equal success.\r
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\n" ); document.write( "\n" ); document.write( "(It is partly a joke,  of course,  but partly is  TRUTH,  in great part . . . )\r
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