http://www.mapleprimes.com/questions/127158-How-To-Solve-A-FirstOrder-IVP-Involving en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Tue, 09 Jun 2026 09:19:41 GMT Tue, 09 Jun 2026 09:19:41 GMT The latest answers and comments added to the Question, How to Solve a First-Order IVP Involving a Constant of Proportionality? http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/questions/127158-How-To-Solve-A-FirstOrder-IVP-Involving http://www.mapleprimes.com/questions/127158-How-To-Solve-A-FirstOrder-IVP-Involving?ref=Feed:MaplePrimes:How to Solve a First-Order IVP Involving a Constant of Proportionality?:Comments#answer127170 <p>Numerically you can get an answer by using dsolve only, but the solution is found only between 0 and 1/2:</p> <p>resNum:=dsolve({diff(y(t),t) = k*(y(t)-10), y(0)=70, y(1/2)=50},numeric,output=listprocedure);<br>K,Y:=op(eval([k,y(t)],resNum));<br>K(.3);<br>plot(K,0..1,-1..0);<br>plot(Y,0..1);<br>#More natural is it to do the following, variants of which you have probably already tried.<br>resEx:=dsolve({diff(y(t),t) = k*(y(t)-10), y(0)=70});<br>solve(eval(resEx,{y(t)=50,t=1/2}),{k});<br>eval(resEx,%);<br><br></p> <p>Numerically you can get an answer by using dsolve only, but the solution is found only between 0 and 1/2:</p> <p>resNum:=dsolve({diff(y(t),t) = k*(y(t)-10), y(0)=70, y(1/2)=50},numeric,output=listprocedure);<br>K,Y:=op(eval([k,y(t)],resNum));<br>K(.3);<br>plot(K,0..1,-1..0);<br>plot(Y,0..1);<br>#More natural is it to do the following, variants of which you have probably already tried.<br>resEx:=dsolve({diff(y(t),t) = k*(y(t)-10), y(0)=70});<br>solve(eval(resEx,{y(t)=50,t=1/2}),{k});<br>eval(resEx,%);<br><br></p> 127170 Sat, 29 Oct 2011 12:05:27 Z Preben Alsholm Preben Alsholm